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>

docs/src/extensions/context-servers.md

@@ -6,7 +6,7 @@ Extensions may provide [context servers](../ai/mcp.md) for use in the Assistant.
 
 To see a working example of an extension that provides context servers, check out the [`postgres-context-server` extension](https://github.com/zed-extensions/postgres-context-server).
 
-This extension can be [installed as a dev extension](./developing-extensions.html#developing-an-extension-locally) if you want to try it out for yourself.
+This extension can be [installed as a dev extension](./developing-extensions.md#developing-an-extension-locally) if you want to try it out for yourself.
 
 ## Defining context servers
 

docs/src/extensions/slash-commands.md

@@ -6,7 +6,7 @@ Extensions may provide slash commands for use in the Assistant.
 
 To see a working example of an extension that provides slash commands, check out the [`slash-commands-example` extension](https://github.com/zed-industries/zed/tree/main/extensions/slash-commands-example).
 
-This extension can be [installed as a dev extension](./developing-extensions.html#developing-an-extension-locally) if you want to try it out for yourself.
+This extension can be [installed as a dev extension](./developing-extensions.md#developing-an-extension-locally) if you want to try it out for yourself.
 
 ## Defining slash commands