After migrating from an old laptop running High Sierra to a new laptop with Monterey and Safari 15.3, Safari didn't reopen windows on startup. I could manually re-copy various files from the old laptop before running Safari, and it would open them on launch, but would reopen with each window having only one tab, set to the startup page (in my case, blank). This turned out to be a known issue for some users, as documented in Apple support forum posts, and confirmed by Apple. I found that if I re-copied the files, launched Safari, then went to each window and opened and closed some tabs, then if I quit and re-ran Safari, it would open one of the windows correctly, but none of the others, and would only do it once.
I tried the solution described here, but the specified files didn't exist for me.
I wiped the drive, re-installed Monterey, re-migrated everything from the old machine, but it behaved exactly the same. So I created a Big Sur installer, wiped the drive, installed Big Sur, re-migrated the data, and Safari worked correctly. At one point I OKed a software update, thinking it was updating Big Sur to 11.6.something, but it actually updated Safari to 15.3 (which I wouldn't have OKed if I'd noticed). To my surprise, Safari 15.3 continues to reopen windows on launch. I might try updating to Monterey again, but only after creating a good backup and having some time to redo everything if need be.