Check nix flake in CI

[jdetter]

Description of Changes

Split out from #3486

Context from @gefjon:

This is caused by recursive cargo build in the CLI tests

Plausible paths forward:

1. I spend several hours figuring out how to make recursive cargo work under Nix.
2. We rewrite the CLI tests to not use recursive cargo, and instead to just call the CLI's entry point as a Rust function.
3. We skip the CLI tests in nix flake check.
4. We give up on checking our flake in CI, it remains broken, and every couple months I lose a day or two of engineering time because some PR breaks my development environment.

API and ABI breaking changes

None, this is just a CI improvement.

Expected complexity level and risk

1 - this is just a CI improvement

Testing