I have had a similar problem, when I shut down my machine and come back a day later, it opens with no old tabs despite also having it set to restore tabs. I found a solution. Safari 15 saves the saved tabs in a new location in comparison to previous versions. So the Lastsession.plist file won't help here (it did help me when I updated to 15 and lost the tabs). Instead, you need to be able to restore files (e.g., from Time Machine) to here:
~/Users/[user name]/Library/Containers/com.apple.Safari/Data/Library/Safari
There are three files that start with "SafariTabs.db" and all three have to be restored for it to work, but it did!
I got this advice from https://www.reddit.com/r/Safari/comments/pvcz1v/safari_15_and_lastsessionplist/heb0yre/, user SeraCarina gets the credit.
I don't yet know whether this glitch is a one-off or I'll be doing this until Apple fixes it. I have just grabbed the 15.1 beta so that may help (but it didn't fix the issue that was in place, hopefully it won't perpetuate it).
I also feel like it may be a Catalina/Safari15 issue. Only just from finding others with the issue, they seem to be on Catalina, lots don't have this problem. But this conclusion could be wrong. I just happen to also be on Catalina.