Give check-changeset job write permissions on pull requests

[dlarocque]

This fixes an issue where a step fails with a 403 for no write permissions: https://github.com/firebase/firebase-js-sdk/actions/runs/13706506246/job/38332961549

[changeset-bot]

⚠️ No Changeset found

Latest commit: dcb983f

Merging this PR will not cause a version bump for any packages. If these changes should not result in a new version, you're good to go. If these changes should result in a version bump, you need to add a changeset.

This PR includes no changesets

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[google-oss-bot]

Size Report ¹

Affected Products

No changes between base commit (5611175) and merge commit (392c599).

Test Logs

• Base (5611175): https://github.com/firebase/firebase-js-sdk/actions/runs/13706192119
• Merge (392c599): https://github.com/firebase/firebase-js-sdk/actions/runs/13706759855

1. https://storage.googleapis.com/firebase-sdk-metric-reports/UD8BDeaJdk.html

[google-oss-bot]

Size Analysis Report ¹

Affected Products

No changes between base commit (5611175) and merge commit (392c599).

Test Logs

• Base (5611175): https://github.com/firebase/firebase-js-sdk/actions/runs/13706192119
• Merge (392c599): https://github.com/firebase/firebase-js-sdk/actions/runs/13706759855

1. https://storage.googleapis.com/firebase-sdk-metric-reports/XYyGsXaN2O.html