Summary

Fixes #3136 by lowering the required OAuth scope from repo to public_repo for the six repository write tools the issue identifies as public-repo-safe:

• add_issue_comment
• issue_write
• create_branch
• push_files
• create_pull_request
• fork_repository

An OAuth deployment that only needs to contribute to public repositories can now request least-privilege public_repo instead of the broad repo scope (which also grants private-repository access).

Why this is safe

• NewTool derives AcceptedScopes through the existing hierarchy (ExpandScopes: repo is a parent of public_repo), so a full repo token still satisfies every one of these tools — no regression for existing deployments.
• No API handler changes; GitHub continues to enforce actual per-repository permissions at the API layer. This only stops the scope filter from hiding tools that public-only tokens could legitimately use.

Testing

• New focused coverage in pkg/github/public_repo_scope_test.go:
  • TestPublicRepoWriteToolsDeclareLeastPrivilegeScopes asserts each tool advertises required: [public_repo] and accepted: [public_repo, repo].
  • TestPublicRepoWriteToolsVisibleToPublicRepoToken asserts the PAT tool filter (CreateToolScopeFilter) shows every tool to a public_repo-only token and keeps it visible for a full repo token.
• go build ./..., go vet ./pkg/github/ ./pkg/scopes/, gofmt clean on changed files.
• Full go test ./pkg/github/ -count=1: no new failures vs a stash-baseline run on clean main (the 6 pre-existing environment-dependent failures reproduce identically on both).