There's a TL;DR at the end.
During the most recent chapter, Kusakabe hypothesizes that the reason Kenjaku was able to bypass Cursed Technique (CT) burnout and keep using his Brain Swap CT even after using his Domain Expansion is because of barrier techniques. In this post, I am going to show how all the pieces for this power system mechanic have already been laid out and explain what exactly Kenjaku did with barriers.
Firstly, it is in the fanbook that we first hear of the concept of "using your body as a domain." When asked why Hanami isn't just creating roots inside other sorcerers, Gege answers that the body of sorcerers is like a domain so you cannot use techniques inside it; you can only create them outside and then pierce the barrier of the body.
This concept is officially introduced in the manga in chapter 208 when Kenjaku explains how he survived Yuki's black hole:
What that means is that using the outline of his body as a barrier, he imbued Antigravity System as a sure hit inside his body, which makes only his body not be affected by gravity. We know that Antigravity System has limits (the reversal, for example, can only be activated for about 6 seconds before a cooldown), but as a sure hit, there would be no limit on the activation time and interval.
Even though that was the first explicit mention of the concept, it has been used throughout the story.
Mahito is the best example of this. Idle Transfiguration activates when the caster touches the target with the palm of their hand. However, Mahito seemingly doesn't require this condition when he is the target of the CT. That is because he is using his body as a domain to imbue Idle Transfiguration as a sure hit on it, which removes the activation requirement of Idle Transfiguration, the touch. (As a side note, Naoya and Naobito are doing the same thing with Projection Sorcery to activate the 24 frames rule on themselves without having to touch themselves with their palm.)
Kokichi in chapter 81 and 82 uses Simple Domain bullets to harm Mahito's soul. At first glance, this doesn't make much sense as Simple Domain cannot neutralize CTs like Domain Amplification can (as stated in the chapter 247 author comment and chapter 254 by Kusakabe). However, Kenjaku spells out the reason why this works: Simple Domain activated inside another domain has the ability to neutralize the sure hit of the domain. If Mahito is using his body as a domain to have Idle Transfiguration as a sure hit inside his body and therefore maintain the shape of his soul without touching himself with his palm, then Simple Domain activated inside his body would nullify his ability to maintain the shape of his soul. The damage done by the exploding bullet would therefore act on both the body and the soul because Mahito is momentarily no longer able to maintain the shape of his soul.
In chapter 123 during Nobara vs. clone Mahito, clone Mahito states that even though he can transfigure his own body, he cannot use transfiguration outside the body. That is because main Mahito imbued Idle Transfiguration in the clone Mahito's body beforehand, so clone Mahito doesn't have access to the technique itself but can still use it due to it being imbued in his body's barrier.
This concept of imbuing your CT in a barrier so you can keep using it even when you don't have access to it was first explicitly mentioned in chapter 227. In it, Gojo explains that Sukuna imbued Shrine in Malevolent Shrine so that he can keep using Domain Amplification or the Ten Shadows Technique simultaneously with Malevolent Shrine.
All the scattered pieces of information have been laid out so we can deduce what exactly Kenjaku did to bypass CT burnout.
Kenjaku always has Brain Swap imbued in his body's domain. When he activates his Domain Expansion, all three of his CTs become burned out (Cursed Spirit Manipulation, Antigravity System, and Brain Swap), but because the Brain Swap CT was imbued in his body's barrier, it can continue to function as it no longer requires input from Kenjaku. This makes it seem as though Brain Swap didn't burn out, but it did.
This explains why Kenjaku said that the trick he pulled against Yuki's black hole was a gamble. For the first time in who knows how long, he removed Brain Swap from his body's domain sure hit and put Antigravity System as the sure hit. This means that if he didn't do it fast and precise enough, he would have become paralyzed for a short interval of time, and the black hole would have crushed him.
TL;DR: The outline of the body of a sorcerer can act as a barrier, and the sorcerer can use their body as a domain by imbuing a CT as a sure hit in it. We know from Sukuna that once you imbue a CT in a barrier, you no longer need to actively maintain that CT. Therefore, Kenjaku has imbued Brain Swap in his body's domain so it remains active even when the Brain Swap CT itself is in burnout.
During the most recent chapter, Kusakabe hypothesizes that the reason Kenjaku was able to bypass Cursed Technique (CT) burnout and keep using his Brain Swap CT even after using his Domain Expansion is because of barrier techniques. In this post, I am going to show how all the pieces for this power system mechanic have already been laid out and explain what exactly Kenjaku did with barriers.
Firstly, it is in the fanbook that we first hear of the concept of "using your body as a domain." When asked why Hanami isn't just creating roots inside other sorcerers, Gege answers that the body of sorcerers is like a domain so you cannot use techniques inside it; you can only create them outside and then pierce the barrier of the body.
This concept is officially introduced in the manga in chapter 208 when Kenjaku explains how he survived Yuki's black hole:
What that means is that using the outline of his body as a barrier, he imbued Antigravity System as a sure hit inside his body, which makes only his body not be affected by gravity. We know that Antigravity System has limits (the reversal, for example, can only be activated for about 6 seconds before a cooldown), but as a sure hit, there would be no limit on the activation time and interval.
Even though that was the first explicit mention of the concept, it has been used throughout the story.
Mahito is the best example of this. Idle Transfiguration activates when the caster touches the target with the palm of their hand. However, Mahito seemingly doesn't require this condition when he is the target of the CT. That is because he is using his body as a domain to imbue Idle Transfiguration as a sure hit on it, which removes the activation requirement of Idle Transfiguration, the touch. (As a side note, Naoya and Naobito are doing the same thing with Projection Sorcery to activate the 24 frames rule on themselves without having to touch themselves with their palm.)
Kokichi in chapter 81 and 82 uses Simple Domain bullets to harm Mahito's soul. At first glance, this doesn't make much sense as Simple Domain cannot neutralize CTs like Domain Amplification can (as stated in the chapter 247 author comment and chapter 254 by Kusakabe). However, Kenjaku spells out the reason why this works: Simple Domain activated inside another domain has the ability to neutralize the sure hit of the domain. If Mahito is using his body as a domain to have Idle Transfiguration as a sure hit inside his body and therefore maintain the shape of his soul without touching himself with his palm, then Simple Domain activated inside his body would nullify his ability to maintain the shape of his soul. The damage done by the exploding bullet would therefore act on both the body and the soul because Mahito is momentarily no longer able to maintain the shape of his soul.
In chapter 123 during Nobara vs. clone Mahito, clone Mahito states that even though he can transfigure his own body, he cannot use transfiguration outside the body. That is because main Mahito imbued Idle Transfiguration in the clone Mahito's body beforehand, so clone Mahito doesn't have access to the technique itself but can still use it due to it being imbued in his body's barrier.
This concept of imbuing your CT in a barrier so you can keep using it even when you don't have access to it was first explicitly mentioned in chapter 227. In it, Gojo explains that Sukuna imbued Shrine in Malevolent Shrine so that he can keep using Domain Amplification or the Ten Shadows Technique simultaneously with Malevolent Shrine.
All the scattered pieces of information have been laid out so we can deduce what exactly Kenjaku did to bypass CT burnout.
Kenjaku always has Brain Swap imbued in his body's domain. When he activates his Domain Expansion, all three of his CTs become burned out (Cursed Spirit Manipulation, Antigravity System, and Brain Swap), but because the Brain Swap CT was imbued in his body's barrier, it can continue to function as it no longer requires input from Kenjaku. This makes it seem as though Brain Swap didn't burn out, but it did.
This explains why Kenjaku said that the trick he pulled against Yuki's black hole was a gamble. For the first time in who knows how long, he removed Brain Swap from his body's domain sure hit and put Antigravity System as the sure hit. This means that if he didn't do it fast and precise enough, he would have become paralyzed for a short interval of time, and the black hole would have crushed him.
TL;DR: The outline of the body of a sorcerer can act as a barrier, and the sorcerer can use their body as a domain by imbuing a CT as a sure hit in it. We know from Sukuna that once you imbue a CT in a barrier, you no longer need to actively maintain that CT. Therefore, Kenjaku has imbued Brain Swap in his body's domain so it remains active even when the Brain Swap CT itself is in burnout.