Hi Seth,
Okay, on your phone the power button is on a cable with all the other buttons, which intersects the charging coil. I've had the bad luck to damage one of those cables on a phone where the battery stretch adhesive broke and I had to try and work the battery out with other methods. I can't say that's what happened to you, but it might be something to consider. The only way to check is to remove the battery again, and yes, I know exactly what a pain in the wazoo it is. Here's what the assembly looks like.
Anyway, as far as replacing it, I've already written everything you'd need to know about doing so in another question, so I'm just going to refer you there for now.
Power button replacement guide - iPhone 12 - iFixit
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