Probably ten years ago with name.com I had a .at domain expire.

I caught it like a day or two later, and successfully renewed it through their site but it did not take.

There was somehow already someone up squatting my domain. I contacted support and they told me there's apparently no renewal window for .at but they could recover it for $140 - oof .. sure. It was nothing super important but would be annoying to lose.

Then it took like a week for them to get back to me, but after that week I got my domain back. I have no idea what gymnastics happened on their side.

That sounds like name.com was squatting on your expired domain and extorted $140 from you to get it back.