Firefox syncs across devices as well, if you sign up for a Firefox account and enable sync. This works for bookmarks, logins, history, and you can even access remote tabs if you want. It's also easy to send a single page from one device to another.
On desktop, Firefox has an import feature that will pull your bookmarks and logins m other browsers (like Chrome) into your Firefox profile.
Even if you're neck-deep in Google services, Chrome doesn't do anything special.
Arc has floated this idea. Currently Arc is Chromium-based, but they say they've designed it to allow for swapping engines in the future.
IIRC, Edge had a similar feature for a while, allowing you to run legacy Internet Explorer tabs if a site required it. Not sure if that still exists.