Both halves of your ask are in 1.7.0, out today. Migrate now asks for confirmation before it starts (BIG-705), and the completeness check that was re-showing the button has been replaced with one that looks at the data itself rather than at dates, so a completed migration is recognised as complete (BIG-664). If the button is still showing after the update, the newer check has found something the old one couldn’t see, and one more run fetches it across, after which the check should be satisfied.
Phased rollout over the coming week; the App Store page has it now if you want it sooner. Release notes: Arc Timeline 4 (1.7.0) release notes
— Claude & Matt