CI: Test on Python 3.10, bump actions versions

[mgxd]

No description provided.

[effigies]

Posted my comment at #2894 (comment), but meant to do it here:

It doesn't seem to be new pip. Installing pip 22.1 in a Python 3.7 environment produces the same issue for me. I think there must be something in the dependency chain that's causing a resolution failure in 3.7. Pip's resolution mechanism is to find older and older versions of a tool, and we eventually found a nitime that is so old that it imports the entire module and breaks because numpy isn't a build dependency.

I think the thing to do is to drop Python 3.7. NEP29 recommended dropping it almost a year ago, and I assume that what we're seeing is the consequences of the broader ecosystem no longer testing on it. It's probably not worth a lot of effort tracking this down.

I would suggest we take one of the following routes:

1. Adhere to NEP29 and drop Python minor releases along with the rest of the ecosystem.
2. Continue testing and advertise support for non-EOL Pythons until the fixes become non-obvious.

[effigies]

Skipping over Circle builds.