Partially revert google#1576 (google#1700)

The GitHub action added in google#1576 fails because it cannot run with the
necessary permissions: it requires write access to be able to post a
comment, but when triggered from a fork, the token is limited to read
access.

The error is from the thollander/actions-comment-pull-request action:

No comment has been found with asked pattern. Creating a new comment.
    Error: Resource not accessible by integration

The downgrading of the token is explained on:

https://docs.github.com/en/actions/security-guides/automatic-token-authentication

where “Maximum access for pull requests from public forked repositories”
says that the pull-requests permission is capped at read in the typical
case for us.

I kept the underlying functionality since we might want to use it for
something else (perhaps track the duration in the README).

Fixes the errors seen on the recent PRs: google#1693, google#1687, and likely
others.