ci: Check for broken links (#30844)

This PR fixes some broken links that where found using
[lychee](https://github.com/lycheeverse/lychee/) as discussed today with
@JosephTLyons and @nathansobo at the RustNL hackathon. Using
[lychee-action](https://github.com/lycheeverse/lychee-action/) we can
scan for broken links daily to prevent issues in the future.
There are still 6 broken links that I didn't know how to fix myself.
See https://github.com/thomas-zahner/zed/actions/runs/15075808232 for
details.

## Missing images

```
Errors in ./docs/src/channels.md

    [ERROR] file:///home/runner/work/zed/zed/docs/.gitbook/assets/channels-3.png | Cannot find file
    [ERROR] file:///home/runner/work/zed/zed/docs/.gitbook/assets/channels-1.png | Cannot find file
    [ERROR] file:///home/runner/work/zed/zed/docs/.gitbook/assets/channels-2.png | Cannot find file
```

These errors are showing up as missing images on
https://zed.dev/docs/channels
I tried to search the git history to see when or why they were deleted
but didn't find anything.

## ./crates/assistant_tools/src/edit_agent/evals/fixtures/zode/prompt.md

There are three errors in that file. I don't fully understand how these
issues were caused historically. Technically it would be possible to
ignore the files but of course if possible we should address the issues.
 
Release Notes:

- N/A

---------

Co-authored-by: Marshall Bowers <git@maxdeviant.com>
Co-authored-by: Ben Kunkle <ben@zed.dev>

.github/actions/build_docs/action.yml

@@ -19,6 +19,12 @@ runs:
       shell: bash -euxo pipefail {0}
       run: ./script/linux
 
+    - name: Check for broken links
+      uses: lycheeverse/lychee-action@82202e5e9c2f4ef1a55a3d02563e1cb6041e5332 # v2.4.1
+      with:
+        args: --no-progress './docs/src/**/*'
+        fail: true
+
     - name: Build book
       shell: bash -euxo pipefail {0}
       run: |