Macbook Pro 16 Failed to boot after Big Sur update now I'm unable to mount the disk even in recovery mode
The 16 MacBook Pro is Intel based and has the T2 chip. This means all the data is well encrypted and the keys are stored on the T2 and the system will unlock all of the system data in target mode and other pass phrases may also be able to decrypt the data with FileVault enabled.
I would revive the firmware if you can’t use your known passwords to try and transfer (but not run first aid) to a second Mac.

https://support.apple.com/en-om/guide/apple-configurator-2/apdebea5be51/mac

Do not restore - the steps are very similar and the words sound too close for comfort. Restore intentionally deletes and destroys all data.
Revive leaves your data intact. Now, if your data is already gone, you won’t know until after the revive  is done. It’s unlikely revive will make it harder or more expensive to do data recovery, but I would stop immediately with any fsck since that deletes files and restores the system to a previous state to make the filesystem correct. It’s the opposite of what you want to get files backed up.
For that you want these:

https://drivesaversdatarecovery.com/
https://www.prosofteng.com/mac-data-recovery and two external drives, one about 16 GB or larger to install a rescue OS from recovery and a second the same size or bigger than your SSD to copy off files. (If you have or can borrow a second Mac, install this there and boot yours in target disk mode.)

Then once you have the files backed up, use Internet Recovery to try reinstalling macOS on top of your existing data (this also doesn’t intentionally erase the data, just layers a working system on top of whatever system was there). With luck, you’ll get a backup and a working system without having to do an erase install or the full restore operation.