It does mean you should use Hetzner from the beginning, because the Hetzner egress bandwidth costs will not eat you alive. But what's with cloud, anyway? Hetzner Cloud is for cheap VPSes. Get a real server at Hetzner and you also get way more compute and storage for the same price as any cloud, as long as the higher price floor doesn't bother you. (There are no $5/mo dedicated servers. Even Raspberry Pi hosting usually costs more than that.)
Depends on what you're doing. If you're running conferencing, there's no data to migrate, so it should be possible to move to somewhere with reasonable bandwidth costs and save money easily, if it's just vms.
If you're doing media sharing, maybe don't migrate data all at once, but upload new stuff to the new place, and at some point move downloads of old stuff on demand: users make request to new place, new place fetches from old place, saves and sends to user --- you were going to pay that egress to users anyway and now you won't have to pay it again.
If you've amassed a giant database that would otherwise never leave, then yeah, that's going to be expensive to move... But maybe you can get a free egress to leave offer?
Note that I think Hetzner includes 'unlimited' egress on dedicated machines, not on cloud vms; but their per TB prices are much more reasonable than big cloud's per GB prices.
>I'm shocked DOJ has not gone after cloud providers
Well, I think so far only Europe has forced free data export if you're changing providers. We'll see if they continue. I won't hold my breath over DOJ...