Recents folder is empty after each restart

The Recents folder is something over which you have no control. It may show thousands of files, or none at all - as in this case.

FWIW, I always remove Recents from my Sidebar, as it is useless.

Instead, you can use the wonderful Smart Folder capability to create one or more, using the precise criteria that you want, so they always show what you want and nothing else.

For example: you may have a smart folder for PDF files opened in the last two days; or image files of any kind, or only png and jpeg, with such and such sizes, and dates... and it is so easy.

Just initiate a search, adjust the criteria, and save. They can be right there on your sidebar to use whenever you want.

Here is an example.

All you have to do is to click Save and check the box that reads "Add to Sidebar" - and there you have it: your version of recent pdf (of course you can vary the criteria to suit your needs, the possibilities are endless).

" One Size does Not fit All  "

If the new computer is going to be the Apple Silicon M1 / M2 Equipped Computer - would suggest Only Migrating the User Account and nothing more.

Some have had success.

Others have been left with a mess when Migrating everything.

1 - Issues that may exist on the older computer, when the Time Machine Backup was made , will be migrated to the New Computer. This would badly pollute the new Original and Pristine installation of the new OS.

2 -  Applications, extensions and Software Drivers may or may not even work on the new computer.

3 - IMHO - it would be best to only install new application etc Directly from the Developer or the Apple Apps Store.

4 - Due Diligence on New Applications and make sure they are Ventura / Monterey / Big Sur compatible and factor in the ARMs CPU of the Apple Silicon Computer  

5 - Worst case and from Apple How to erase all content and settings - Apple Support (CA)

6 - Start afresh without the Baggage form the previous version of macOS.

7 - One can always us Time Machine Backup to Restore Individual Files at a later date

Welcome.

Whether or not the user does the Erase All Content and Setting is a user choice.

Though, much like the same process in iOS - the version of the Operating System will remain and is Untouched by this process.

Much more streamed lined then back in the " Olden Days " with Intel Equipped machines. ( Humour here )

Have done this route but once when trading in a M1 MBA for the M2 MBA.

Took about 20 minutes and presto and viola - all done.

Well, then why not create your own?

Just search for date last opened is in the last week, or whatever. There is your own Recents.