Start PR checks on bot-created PRs

[Suleimanlatrsh]

WHY are these changes introduced?

Bot PRs from maintenance-prs and gardener-backlog-prs get no CI. They are opened with GITHUB_TOKEN, and GitHub does not start pull_request workflows for events made with that token. For example, #8751 shows "No checks reported". Today the gardener has to close and reopen each PR to start the tests.

WHAT is this pull request doing?

• tests-pr.yml: adds a workflow_dispatch trigger. The graphql-codegen check now also runs on dispatch. Without that it would be skipped, and a skipped required check counts as passing.
• maintenance-prs.yml and gardener-backlog-prs.yml: add a start-pr-checks job that runs after the agent. If the run opened a PR, the job dispatches tests-pr.yml on the PR branch. The resulting check runs attach to the PR's head commit, the same way /snapit works since Restore /snapit using workflow dispatch #8721.
• actions: write is only granted to the new job, not the agent's job. Otherwise the agent could dispatch other workflows such as release.yml.

Type-diff, breaking change detection and the E2E jobs still skip on dispatch because they need pull_request context. None of them are required checks.

How to manually test your changes?

workflow_dispatch only works once the trigger is on main, so this can't be fully tested before merge. What I checked:

• actionlint passes on all three files.
• I ran the maintenance PR filter against the live open PR list with run ID 37247687073. It matched exactly the 4 PRs from that run ([Tests] Cover DoctorSuite filesystem assertions #8748 to [Refactor] Count deploy errors per extension with a Map #8751).

After merge, run maintenance-prs from the Actions tab. Each new PR should show the PR checks without a close and reopen.

Checklist

• I've considered possible cross-platform impacts (Mac, Linux, Windows)
• I've considered possible documentation changes
• I've considered analytics changes to measure impact
• The change is user-facing — I've identified the correct bump type (patch for bug fixes · minor for new features · major for breaking changes) and added a changeset with pnpm changeset add