Not the commenter you were replying to, but I have both a Kindle and a X4. No, it does not, but searching for a unique enough phrase (just two or three words) on the current page gets you there fast enough.

If you install koreader on the kobo, crosspoint on the x4 and create a free koreader sync account (or host your own sync sever): yes - but on the x4 you need to manually trigger syncs

Alternatively if you wish to stick with the stock Kobo reader app it is possible to sync via a https://grimmory.org/ instance

As someone who also juggles multiple readers, I find it easier to have a different book per device. Otherwise I would waste too much time trying to sync between the two.

Yes. I read multiple books in parallel. Each on a different reader. So syncing is not something I usually need though I did build myself a local sync server for fun.