☞ Is there a set of URLs or bookmarks somewhere used by Safari to remember open windows/tabs between sessions?
In macOS Catalina the ~/Library/Safari/LastSession.plist file contains a list of all open windows and their tabs.
Note that while it’s called LastSession.plist, nonetheless, it does contain the current windows and their tabs.
You can try copying this file to the same location on the other Mac and see if it gives you what you want. In case it’s not obvious, Safari needs to be closed when replacing this file.
I tested copying the LastSession.plist file from macOS Catalina to macOS Big Sur and it worked by opening Safari and selecting Reopen All Windows from Last Session from the History menu.
I’m currently using Safari version 14.0.3 (15610.4.3.1.6, 15610) on macOS Catalina and Safari version 14.1.1 (166220.127.116.11.4) on macOS Big Sur.