Well, it's a combination of hype and feats as always. I'll break it down for you.
Mihawk is by far #1 of this group. Marines, Yonko, fellow Shichibukai and Supernova all attest to his strength. He also has some feats that were mad at the time.
Beckmann has the hype of cutting of Kids arm, stopping Kizaru, the statement about Shanks commanders being stronger on average than other yonko commanders and he was specifically mentioned as the first commander amongst the top 3. He also has the distinction of being called Vice Captain and Partner, same as Rayleigh.
Shiryu at the moment has a loss to Magellan who I to be fair believe was supposed to be Admiral level for 4 hours of the day and especially in a confined space like Impel Down. A team of yonko veterans and commanders like Ivankov, Jinbei, Crocodile and Luffy ran from him.
Shiryu who was supposedly close in strength has that going for him so he should be a real power house and a Zoro task. But apart from that, atm we've only seen or heard of him losing, using invisibility to slash a distraught Moriah and stabbing a distracted 80 year old Garp. Thus when we get more he will likely be > Beckmann which in itself is close to how high an underling can rank without becoming yonko themselves.
Its all hype for Mihawk, Mihawk has no on-panel battle with a top tier. His off-panel battle with Pre-Emperor Shanks is not more impressive than DFless Teach's fight with Pre-Emperor Shanks. Even Shiryu has a fight with a top tier on panel which was vs Garp, who was equally fighting with Akainu's equal Aokiji. Thats why I said your reasoning makes no sense when you say Shiryu has only hype then you put Mihawk and Beckman above.
Being Warlord has no hype over Magellan or Shiryu as they were dealing with many Warlords in Impel Down, Magellan even trusted Shiryu to handle another Warlord and set him free for that.
Shanks's commanders are being balanced doesn't mean Beckman is stronger than other top commanders, it means they have no weak points in their commanders, thats what Brannew said, that has nothing to do with Beckman. Thats a hype for their lower level commanders. We see Shanks's allies and their other fodder pirates, they are too weak. To cover up that weakness, all of their low level commanders must be strong. Teach or Kaido wouldn't ally themselves with weak pirates like Shanks does.
Beckman stopped Kizaru for 1 chapter, Marco stopped Kizaru as well. That doesn't give any superiority for Beckman. Marco also stopped more than just Kizaru, stopped Big mom and Akainu as well.
Cutting Kid's arm when Kid was much weaker than his Wano version when Kid was trying to be partners with fodders like Apoo or Hawkins isn't a great hype. Also we have no confirmation Beckman ''alone'' did that, Killer specifically says ''they'' did it not 1 person only.
Except Shiryu didn't lose to Magellan. Ivankov says Shiryu and Magellan are equals in power with Shiryu being the more dangerous of the two. If Shiryu lose to Magellan, why would he say they are equals when Magellan already beat Shiryu? Thats some nonsense produced by butthurt clowns. Shiryu simply surrender without fighting since beating Magellan+entire Impel Down army by himself alone would be impossible.
Shiryu didn't directly attack Moria 1 v 1, Shiryu one-shotted Moria's Zombie army and Moria got hurt by the side effect of his AoE attack.