I’m not sure if tab syncing is actually implemented yet in production. (I use _way_ too many tabs to risk turning that feature on!) They had the check-box for tab syncing there long ago, so that when it _was_ implemented, users who wished to opt-out wouldn’t have to return to the settings. (They probably should have had that line colored in grey or somesuch, but almost the entire public life of Edge Chromium has been during a pandemic so I’m allowing them some extra grace here.)
By checking edge://sync-internals on your first machine (there should be a table in the lower-right? corner of the first tab) you should be able to see how many favorites, passwords, tabs, etc. have been uploaded. Does it show there that any tabs are even being sent to the sync server yet?
That same screen, viewed from each computer, should also show you whether or not sync is done from the perspective of that browser.
Finally, you can always create a new, temporary Edge user profile on either computer and sign in to check syncing with fresh settings … just remember to delete that extra profile when you’re done testing.