I just went through this (the trek started mid-December 2023, and I just finished the "clean-up" work.
The only way (as folks have stated) is to have the 'email' showing you purchased it from Sony or Kobo (and they will only honor Kobo purchases).
What I found (180 books in total, BTW) that no longer showed up in the "archives" or in "purchases" (which is the other place to look per Kobo chat).
If you know the title and author and are entitled, you can still get it, but it is an easter egg hunt. For those, that were curious I easter egg hunted over 120 books.
If you have an old reader "or" you have a long-term Kobo device (e.g., I had a form), you might be able to find some of your old entitled books in caliber under "deleted" or "archived" with a 0-byte reference. With that, I found at least 20 ...
Now folks will say back-up, etc ... and I 100% agree with you. I thought I was okay until last summer when I had a massive power outage due to a Texas monsoon and lost both of my NAS heads due to a freak firmware bug "and" it would have survived the 1st failure if I was home to turn the kit down usually and the system didn't bounce twice.
I have family members looking at me like I am a freak because I took the time to rebuild the entire libraries (kindle and kobo) and reworked it (along with backing it up on two NAS's and three cloud providers
I wish/pray no one else has this happen to them, but if you do ... ping me I can share whatever I learned