feat: implement <ClientFilter /> to AI Bridge request logs (#22694)

Closes #22136

This pull-request implements a `<ClientFilter />` to our `Request Logs`
page for AI Bridge. This will allow the user to select a client which
they wish to filter against. Technically the backend is able to actually
filter against multiple clients at once however the frontend doesn't
currently have a nice way of supporting this (future improvement).

<img width="1447" height="831" alt="image"
src="https://github.com/user-attachments/assets/0be234e2-25f2-4a89-b971-d74817395da1"
/>

---------

Co-authored-by: Jeremy Ruppel <jeremy.ruppel@gmail.com>
Co-authored-by: Claude Sonnet 4.6 <noreply@anthropic.com>

docs/reference/api/aibridge.md

@@ -1,5 +1,38 @@
 # AI Bridge
 
+## List AI Bridge clients
+
+### Code samples
+
+```shell
+# Example request using curl
+curl -X GET http://coder-server:8080/api/v2/aibridge/clients \
+  -H 'Accept: application/json' \
+  -H 'Coder-Session-Token: API_KEY'
+```
+
+`GET /aibridge/clients`
+
+### Example responses
+
+> 200 Response
+
+```json
+[
+  "string"
+]
+```
+
+### Responses
+
+| Status | Meaning                                                 | Description | Schema          |
+|--------|---------------------------------------------------------|-------------|-----------------|
+| 200    | [OK](https://tools.ietf.org/html/rfc7231#section-6.3.1) | OK          | array of string |
+
+<h3 id="list-ai-bridge-clients-responseschema">Response Schema</h3>
+
+To perform this operation, you must be authenticated. [Learn more](authentication.md).
+
 ## List AI Bridge interceptions
 
 ### Code samples