The only known traits of a Zoan transformation are abnormal recovery rate and transformation—Kaido has both: An abnormal recovery rate that goes far beyond what the other Zoans can do and multiple modes of fighting. You can also say awakened Zoans act abnormally due to the influence of their Zoan personality, which can be observed in both Luffy as well as the ID beasts. Kaido displayed abnormal behavior in his modes too.
The only known quality of the Paramecia Awakening is the ability to influence your surroundings with your ability. Big Mom's ability can influence other people's souls. Other than this, narratively speaking, Kaido and Big Mom are supposed to have maxed out their potential, which means they peaked in all areas that they could. Katakuri acted like awakening is something that you'd naturally expect from someone of his caliber. So if it is seemingly a must-have ability for a DF user of Katakuri's caliber who's more of a Haki-reliant fighter than a DF-reliant fighter, then it's only natural the likes of Kaido and Big Mom would possess it—Even Doffy has it, as a matter of fact.
Personally, it makes no sense to me that Kaido is able to match Luffy's awakening without having his own awakening when Luffy's fruit is supposed to have the most broken and OP ability out of all mythical types—It's his awakening, in particular, was hyped to the moon.
Lastly, we have no reason to think they don't have awakening besides the fact that it wasn't vocally mentioned.