Testing: add a CI test using the minimum version of every dependency

Since we don't commit our `Cargo.lock` file, we're always testing with the latest version of every dependency. If we were to accidentally use a feature added after the minimum version specified in `Cargo.toml`, then all our tests would pass, even though some users' builds could fail. We should test (or at least compile -- with `check`?) with the exact version specified in our `Cargo.toml` file.

Start with the dependency versions specified in Cargo.toml and the repository's CI configuration. Determine how to run a test or cargo check against those exact minimum versions, then verify that the CI job succeeds using the minimum dependency set.

Written by the indexing model from the issue text.