I understand what you want to know and why, but I do not shoot 4K, only 5.3K, I don't shoot clips more than a few minutes in length, and I do not shoot underwater. So, I cannot help you. When one shoots short clips like I do, battery life is irrelevant - carrying an extra GoPro battery and switching are not important burdens.
I would suggest searching "Hero 12 underwater video". I found a bunch of videos of people shooting underwater with a Hero 12 and who formerly used a Hero 12. You could ask them in the comments section about battery life. "Fintastic Films" is one example,.
That is better than listening to anyone quoting a site or to somebody, like me, who gets nothing from longer battery life (overheating is another thing).