feat: add GET /api/v2/templatebuilder/bases endpoint (#26116)

Implement `GET /api/v2/templatebuilder/bases`, which returns the list of
base templates available in the template builder. Reads from the bundled
catalog by cross-referencing `templatebuilder.BaseTemplateIDs()` with
`examples.List()`, enriching each entry with the OS from the `exampleID
-> OS` map.

The endpoint is gated behind the template builder feature flag (returns
404 when disabled) and requires `policy.ActionRead` on
`rbac.ResourceTemplate`.

Depends on #26115

> [!NOTE]
> This PR was authored by Coder Agents on behalf of @jeremyruppel.

docs/manifest.json

@@ -1611,6 +1611,10 @@
 							"title": "Tasks",
 							"path": "./reference/api/tasks.md"
 						},
+						{
+							"title": "TemplateBuilder",
+							"path": "./reference/api/templatebuilder.md"
+						},
 						{
 							"title": "Templates",
 							"path": "./reference/api/templates.md"

docs/reference/api/schemas.md

@@ -12046,6 +12046,50 @@ Restarts will only happen on weekdays in this list on weeks which line up with W
 |------------------|------------------------------------------------------|----------|--------------|-------------|
 | `[any property]` | [codersdk.TransitionStats](#codersdktransitionstats) | false    |              |             |
 
+## codersdk.TemplateBuilderBase
+
+```json
+{
+  "description": "string",
+  "icon": "string",
+  "id": "string",
+  "name": "string",
+  "os": "string"
+}
+```
+
+### Properties
+
+| Name          | Type   | Required | Restrictions | Description |
+|---------------|--------|----------|--------------|-------------|
+| `description` | string | false    |              |             |
+| `icon`        | string | false    |              |             |
+| `id`          | string | false    |              |             |
+| `name`        | string | false    |              |             |
+| `os`          | string | false    |              |             |
+
+## codersdk.TemplateBuilderBasesResponse
+
+```json
+{
+  "bases": [
+    {
+      "description": "string",
+      "icon": "string",
+      "id": "string",
+      "name": "string",
+      "os": "string"
+    }
+  ]
+}
+```
+
+### Properties
+
+| Name    | Type                                                                  | Required | Restrictions | Description |
+|---------|-----------------------------------------------------------------------|----------|--------------|-------------|
+| `bases` | array of [codersdk.TemplateBuilderBase](#codersdktemplatebuilderbase) | false    |              |             |
+
 ## codersdk.TemplateBuilderConfig
 
 ```json

docs/reference/api/templatebuilder.md

@@ -0,0 +1,40 @@
+# TemplateBuilder
+
+## List template builder base templates
+
+### Code samples
+
+```shell
+# Example request using curl
+curl -X GET http://coder-server:8080/api/v2/templatebuilder/bases \
+  -H 'Accept: application/json' \
+  -H 'Coder-Session-Token: API_KEY'
+```
+
+`GET /api/v2/templatebuilder/bases`
+
+### Example responses
+
+> 200 Response
+
+```json
+{
+  "bases": [
+    {
+      "description": "string",
+      "icon": "string",
+      "id": "string",
+      "name": "string",
+      "os": "string"
+    }
+  ]
+}
+```
+
+### Responses
+
+| Status | Meaning                                                 | Description | Schema                                                                                   |
+|--------|---------------------------------------------------------|-------------|------------------------------------------------------------------------------------------|
+| 200    | [OK](https://tools.ietf.org/html/rfc7231#section-6.3.1) | OK          | [codersdk.TemplateBuilderBasesResponse](schemas.md#codersdktemplatebuilderbasesresponse) |
+
+To perform this operation, you must be authenticated. [Learn more](authentication.md).