The problem with the stuck power button on brand new iPhone 12 Pro's (and Max's) is common for Apple customers and even Apple employees - with 500 people reporting this persistent quality control problem of brand new iPhone 12s from Nov 2020 to June 2021 in this forum alone.
Spoiler Alert: Don't hesitate, immediately return your iPhone for a new iPhone. Do this before Apple wants to replace your brand new iPhone with a used refurbished phone. My previous experience with Apple's Genius replacing my iPhone with a refurbished iPhone is that the battery didn't work for as long as expected, and the transfer of data was not done completely.
I called Apple support, since I paid $299 for AppleCare+, and I was told that the earliest appointment to try to exchange my broken brand new iPhone 12 Pro for a working brand new iPhone 12 Pro is 2 days out. Worse, the Apple representative said that he had the same problem. Still worse, I was told that they couldn't guarantee that the replacement would be a new iPhone 12 Pro.
I found the article "Cleaning your iPhone" at https://support.apple.com/en-us/HT207123 generally useful but not helpful for this problem. It says: "Use a soft, slightly damp, lint-free cloth—for example, a lens cloth."
I read all of this thread, which includes suggestions on how the power button can sometimes be unstuck, but I didn't want to do any of the questionable solutions for cleaning by splashing with water or brushing with a q-tip damp with alcohol.
Following the instruction on the Apple support page, I tried to "exercise" the stuck power button on my brand new iPhone 12 Pro by sliding my thumb back and forth across the power button with a slightly damp cloth .. it didn't work .. and worse .. my phone called for emergency help before I realized what was happening. I stopped the outgoing call but it was too late and the helpful 911 service called me back to make sure everything was ok, which I assured the operator that everything was fine. I asked the operator how often emergency services got false alarms from iPhones .. and the operator said: "it happens every day". I asked how many times a day this happens, and the emergency services operator said: "I don't know, I'm only one operator and we have many operators."
Summary: The problem gets worse; un-sticking takes customer cleaning methods that aren't recommended; and if you notice that the power button doesn't click (like mine didn't on my brand new phone) that isn't a haptic feature, it's a broken phone.