docs: fix broken and naked relative links (#25825)

Several relative links in the docs pointed at pages that no longer exist
or rendered incorrectly on coder.com.

Fixes:

- `start/first-template.md`: IDE links repointed from the removed
`../ides.md` / `../ides/web-ides.md` to their current homes under
`user-guides/workspace-access/`.
- `tutorials/example-guide.md`: contributing link repointed to
`../about/contributing/documentation.md`.
- `about/contributing/backend.md`: the `migrations/testdata/fixtures`
and `full_dumps` references (and the `000024_example.up.sql` example)
used relative paths that escape `docs/` and render as bogus
`/docs/coderd/...` routes on the site. Normalized to the canonical
`github.com/coder/coder/(blob|tree)/main/...` form already used by ~120
other source links in the docs.
- Normalized extensionless directory links (`ai-coder/ai-gateway`,
`user-guides/workspace-access`, `install`) to their `/index.md` targets
for consistency with the rest of the docs.

This class of bug is invisible to the local doc checks (`make
lint/markdown` / `pnpm check-docs` only run markdownlint + table
formatting); only CI's Linkspector job validates link targets. Found via
a relative-link audit while investigating the docs preview on #25816.

Source-link version-awareness (so older docs versions don't all point at
`main`) is tracked separately in DOCS-268 and will be handled in the
coder.com render layer.


Linear: DOCS-278

Co-authored-by: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

docs/ai-coder/tasks-core-principles.md

@@ -17,7 +17,7 @@ Coder Tasks is Coder's platform for managing coding agents. With Coder Tasks, yo
 
 ![Tasks UI](../images/guides/ai-agents/tasks-ui.png)Coder Tasks Dashboard view to see all available tasks.
 
-Coder Tasks allows you and your organization to build and automate workflows to fully leverage AI. Tasks operate through Coder Workspaces. We support interacting with an agent through the Task UI and CLI. Some Tasks can also be accessed through the Coder Workspace IDE; see [connect via an IDE](../user-guides/workspace-access).
+Coder Tasks allows you and your organization to build and automate workflows to fully leverage AI. Tasks operate through Coder Workspaces. We support interacting with an agent through the Task UI and CLI. Some Tasks can also be accessed through the Coder Workspace IDE; see [connect via an IDE](../user-guides/workspace-access/index.md).
 
 ## Why Use Tasks?
 

docs/ai-coder/tasks.md

@@ -11,7 +11,7 @@ Coder Tasks is an interface for running & managing coding agents such as Claude
 
 ![Tasks UI](../images/guides/ai-agents/tasks-ui.png)
 
-Coder Tasks is best for cases where the IDE is secondary, such as prototyping or running long-running background jobs. However, tasks run inside full workspaces so developers can [connect via an IDE](../user-guides/workspace-access) to take a task to completion.
+Coder Tasks is best for cases where the IDE is secondary, such as prototyping or running long-running background jobs. However, tasks run inside full workspaces so developers can [connect via an IDE](../user-guides/workspace-access/index.md) to take a task to completion.
 
 You can also interact with Coder Tasks from your IDE. The [Coder extension for VS Code](https://marketplace.visualstudio.com/items?itemName=coder.coder-remote) (and compatible forks like Cursor) enables you to create, monitor, and manage Tasks directly from the IDE, eliminating the need to context-switch to a browser. After logging in, you get access to a dedicated Tasks view in the sidebar that lets you select a template, configure parameters, prompt an agent, and track task status or download logs. Your tasks run in Coder workspaces with access to your repos, credentials, and internal network.