chore: Fix permission in release job that creates a new tag

Description

[ ] Bug fix (non-breaking change which fixes an issue). Please, add the "bug" label to the PR.
[ ] New feature (non-breaking change which adds functionality). Please, add the "enhancement" label to the PR. A migration guide must be created or updated if the new feature will go in a major version.
[ ] Breaking change (fix or feature that would cause existing functionality to not work as expected). Please, add the "breaking change" label to the PR. A migration guide must be created or updated.
[ ] This change requires a documentation update
[ ] Documentation fix/enhancement

[x] I have signed the MongoDB CLA
[x] I have read the contributing guides
[x] I have checked that this change does not generate any credentials and that they are NOT accidentally logged anywhere.
[ ] I have added tests that prove my fix is effective or that my feature works per HashiCorp requirements
[ ] I have added any necessary documentation (if appropriate)
[ ] I have run make fmt and formatted my code
[x] If changes include deprecations or removals, I defined an isolated PR with a relevant title as it will be used in the auto-generated changelog.
[x] If changes include removal or addition of 3rd party GitHub actions, I updated our internal document. Reach out to the APIx Integration slack channel to get access to the internal document.