Does erasing the HD and then restoring from time machine backup remove applications? My wife has a 2017 MBP and after upgrading her OS to Big Sur, the laptop has become dog slow. It takes literally seconds for a new program or browser tab to open. The OS should be called 'Big Slow'.
Anyway, I thought I might try erase her HD and reinstall the OS, but we have some concerns.
We want to ONLY reinstall the OS. We do not want to lose any data and we do not want to have to reinstall any applications. She does regular Time Machine backups.
There are a lot of posts with the same question I have here, but for whatever reason, they all ignore the question about applications... so I am asking again.

Will using the 'reinstall OS' option result in DATA being removed?
Will using the 'reinstall OS' option result in APPLICATIONS being
removed?
Must we reinstall the OS and then restore from the Time
Machine backup, or a simple 'reinstall OS' is enough?

Thanks
This is an answer to the question as asked, but I suspect further investigation will be necessary.
Reinstalling the OS without removing existing detritus will quite likely return you to the exact same state.
Reinstall from Recovery without erase will clean up the OS itself without affecting any other data/apps. If the OS itself was at issue, then it will fix the OS. It will not fix anything user-installed that is slowing the OS down.
Erasing then installing from scratch then migrating in from Time Machine will return you to the Mac as you last had it. No change, except the OS cleanup from the previous step.