It only works on desktop, but I use Syncthing to sync the whole profile (with the cache etc folders excluded).
You do need to make sure the profile path is identical on both machines as it’s hardcoded in the extensions json file, and otherwise your extensions won’t work properly.
So long as you close the browser on one machine before opening it on the other, it will sync your open tabs as well.
Now I’m just imagining Pliny the Elder with access to TikTok:
Pliny the Elder, The Natural History - BOOK XXVIII. REMEDIES DERIVED FROM LIVING CREATURES:
https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.02.0137%3Abook%3D28