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/ai/agent-panel.md

@@ -3,7 +3,7 @@
 The Agent Panel provides you with a way to interact with LLMs.
 You can use it for various tasks, such as generating code, asking questions about your code base, and general inquiries such as emails and documentation.
 
-To open the Agent Panel, use the `agent: new thread` action in [the Command Palette](./getting-started.md#command-palette) or click the ✨ (sparkles) icon in the status bar.
+To open the Agent Panel, use the `agent: new thread` action in [the Command Palette](../getting-started.md#command-palette) or click the ✨ (sparkles) icon in the status bar.
 
 If you're using the Agent Panel for the first time, you'll need to [configure at least one LLM provider](./configuration.md).
 

docs/src/configuring-zed.md

@@ -112,7 +112,7 @@ Non-negative `float` values
 
 **Options**
 
-You can find the names of your currently installed extensions by listing the subfolders under the [extension installation location](./extensions/installing-extensions#installation-location):
+You can find the names of your currently installed extensions by listing the subfolders under the [extension installation location](./extensions/installing-extensions.md#installation-location):
 
 On MacOS:
 

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
 

docs/src/languages/json.md

@@ -32,7 +32,7 @@ To workaround this behavior you can add the following to your `.prettierrc` conf
 
 ## JSON Language Server
 
-Zed automatically out of the box supports JSON Schema validation of `package.json` and `tsconfig.json` files, but `json-language-server` can use JSON Schema definitions in project files, from the [JSON Schema Store](https://www.schemastore.org/json/) or other publicly available URLs for JSON validation.
+Zed automatically out of the box supports JSON Schema validation of `package.json` and `tsconfig.json` files, but `json-language-server` can use JSON Schema definitions in project files, from the [JSON Schema Store](https://www.schemastore.org) or other publicly available URLs for JSON validation.
 
 ### Inline Schema Specification
 

docs/src/languages/lua.md

@@ -86,7 +86,7 @@ Then in your `.luarc.json`:
 
 ### Inlay Hints
 
-To enable [Inlay Hints](../configuring-languages#inlay-hints) for LuaLS in Zed
+To enable [Inlay Hints](../configuring-languages.md#inlay-hints) for LuaLS in Zed
 
 1. Add the following to your Zed settings.json:
 

docs/src/languages/markdown.md

@@ -23,7 +23,7 @@ def fib(n):
 
 ### Format
 
-Zed supports using Prettier to automatically re-format Markdown documents. You can trigger this manually via the {#action editor::Format} action or via the {#kb editor::Format} keyboard shortcut. Alternately, you can automatically format by enabling [`format_on_save`](./configuring-zed.md#format-on-save) in your settings.json:
+Zed supports using Prettier to automatically re-format Markdown documents. You can trigger this manually via the {#action editor::Format} action or via the {#kb editor::Format} keyboard shortcut. Alternately, you can automatically format by enabling [`format_on_save`](../configuring-zed.md#format-on-save) in your settings.json:
 
 ```json
   "languages": {