I have had the same issue. After updating, the 15 inch MacBook Pro 2018 couldn't be used when I unplugged the powercable, it turned off and it was a question wether or not I could restart it. Working in a workplace were I have to be in different offices, it was extremely irritating...
I noticed a post on a forum, where it was mentioned that the firmware could be damaged and that I had to contact the apple support center. I phoned and they didn't recognised the problem. While talking to a senior 'problem solver', he said it would be highly inprobable that the firmware would be corrupted by updating to Monterey. After almost an hour, he came to the conclusion that the firmware might be corrupted and that it had to be revived by using another MacBook using a T2 chip, or a clean install OS. Because the installation also puts new firmware on the machine, that might be helping.
In different combinations I did manage to turn on the laptop (close the laptop, take out the powerchord, wait several seconds and put in in the left front (nearest to me) port. Open the laptop and using left CTRL, OPTION, right Shift it started up. Once turning on, the machine keeps working. After a clean install, (at startup push OPTION, CMD, + R) all the problems are gone now...
The biggest challenge was to get the computer to turn on. I tried several things and on several occasions, it turned on using different techniques...
Hope it works for you....
Hope