Partially revert #1576 (#1700)

The GitHub action added in #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: #1693, #1687, and likely
others.

.github/workflows/course-schedule.yml

@@ -1,27 +0,0 @@
-name: "Course Schedule Updates"
-on:
-  pull_request:
-    paths:
-      - "src/**.md"
-
-jobs:
-  course-schedule:
-    runs-on: ubuntu-latest
-    name: Make Course Schedule Comment
-    permissions:
-      pull-requests: write
-    steps:
-      - name: Checkout
-        uses: actions/checkout@v4
-
-      - name: Setup Rust cache
-        uses: ./.github/workflows/setup-rust-cache
-
-      - name: Generate Schedule
-        run: cargo run -p mdbook-course --bin course-schedule > course-schedule.md
-
-      - name: Comment PR
-        uses: thollander/actions-comment-pull-request@v2
-        with:
-          filePath: course-schedule.md
-          comment_tag: course-schedule