We do not need to enable "write" permission because we are not using the auto-fix feature but we could enable this two permissions:
permissions:
pull-requests: write
statuses: write
The first one makes this kind of comment on the PR:

And the second one is used by MegaLinter
[GitHub Status Reporter] Error posting Status for SPELLwith cspell: 403
GitHub API response: {"message":"Resource not accessible by integration","documentation_url":"https://docs.github.com/rest/reference/repos#create-a-commit-status"}
to post a status on the pull request for each processed linter.
We do not need to enable "write" permission because we are not using the auto-fix feature but we could enable this two permissions:
The first one makes this kind of comment on the PR:
And the second one is used by MegaLinter
to post a status on the pull request for each processed linter.