Unexpected Shut Down MacBook Pro 2017 battery full Mac OS Monterey 12.1

Try an SMC Reset.

Run the Apple Diagnostics to see if any hardware issues are detected.

Disconnect all external devices in case one of them is causing a problem.

You may need to have Apple or an Apple Authorized Service Provider examine the laptop to provide you with a repair estimate. If you have a non-Touchbar model, then it may qualify for a free Battery repair program:

https://support.apple.com/13inch-macbookpro-battery-replacement

FYI, here is the current list of the publicly acknowledged free repair programs for various Apple products (some products have multiple programs):

https://support.apple.com/service-programs

It is really hard to say since these USB-C Apple laptops act very weird in regards to power & battery. I've had several of our organization's laptops have trouble powering on especially after an SMC Reset recently. It is also not unusual to have a battery with significant charge not power on without first connecting the charger.

It is the unexpected shutdowns you have that are a concern. To look for a possible software issue run EtreCheck and post the report here using the "Additional Text" icon which looks like a piece of paper. If you give EtreCheck "Full Disk Access", then the summary of the recent logs will also be included which may contain useful information. You can also see how the laptop works when booted into Safe Mode which disables login items and third party drivers as well as deleting some temp & cache files.

If you feel it is a Monterey only issue, then you can perform a clean install of macOS Big Sur by first erasing the whole physical drive. Just make sure to have a good backup since erasing the drive will destroy all data on the drive. Also if you are using Time Machine as a backup, then I don't believe you will be able to restore a Monterey TM backup to Big Sur so make sure any new or modified files since you installed Monterey should be stored on external media in a format that any OS can access.