This is a follow-up to 1dafa890, where
Goreleaser doesn't yet have an image based on Go 1.22 so we can't build
the project.

We can allow `GOTOOLCHAIN=auto` to auto-download SDKs as necessary.

As per [0], we also need to make sure that we've got the explicit patch
version in our `go.mod.`

[0]: https://github.com/golang/go/issues/62278#issuecomment-1933790368