chore: use go mod tidy instead of tidied - #2482

Greptile Summary

This PR replaces the external tidy checker with Go's built-in tidy diff mode. The main changes are:

• Root tidy-ci now runs go mod tidy -diff.
• Example module tidy-ci now runs go mod tidy -diff.
• Internal test module tidy-ci now runs go mod tidy -diff.

Confidence Score: 5/5

This looks safe to merge.

• No blocking issues found in the changed code.

_{Reviews (3): Last reviewed commit: "chore: use go mod tidy instead of tidied" | Re-trigger Greptile}

Per Greptile - does this run go mod tidy then exit if its out of sync, or only checks if it's out of sync?

Edit: rereviewing should be OK as tidy-ci only affected

We'll also need to remove https://github.com/oapi-codegen/actions/blob/0b10ad68a53148bd29896be82ad92027b35507a3/.github/workflows/ci.yml#L107-L108