feat: add chat summary tab in the right sidebar and per-chat cost endpoint (#26649)

Stacked on #26657 (the persisted whole-chat summary backend). Base
branch is `chat-summary-62j9`; review/merge that first.

Adds a reusable `ChatSummary` component.

The summary text is the persisted whole-chat summary (`chat.summary`)
introduced by #26657. It is generated asynchronously and may be `null`
until the first summary is produced, in which case the popover renders a
muted empty state. Live updates arrive via that PR's
`chat_summary_change` watch event, which is already merged into the chat
caches.

Cost is served by a new per-chat endpoint, `GET
/api/experimental/chats/{chat}/cost`, which rolls up assistant-message
cost across a chat's root and child (subagent) chats and is authorized
like the other `{chat}` routes (read on the chat, 404 otherwise).

Visual and interaction coverage lives in `ChatSummary.stories.tsx` and
`ChatSummaryPopover.stories.tsx` (including populated-summary,
empty-state, and cost-loading cases).

---------

Co-authored-by: Cursor <cursoragent@cursor.com>

docs/reference/api/chats.md

@@ -1283,6 +1283,48 @@ Experimental: this endpoint is subject to change.
 
 To perform this operation, you must be authenticated. [Learn more](authentication.md).
 
+## Get chat cost
+
+### Code samples
+
+```sh
+# Example request using curl
+curl -X GET http://coder-server:8080/api/experimental/chats/{chat}/cost \
+  -H 'Accept: application/json' \
+  -H 'Coder-Session-Token: API_KEY'
+```
+
+`GET /api/experimental/chats/{chat}/cost`
+
+Experimental: this endpoint is subject to change.
+
+### Parameters
+
+| Name   | In   | Type         | Required | Description |
+|--------|------|--------------|----------|-------------|
+| `chat` | path | string(uuid) | true     | Chat ID     |
+
+### Example responses
+
+> 200 Response
+
+```json
+{
+  "chat_id": "efc9fe20-a1e5-4a8c-9c48-f1b30c1e4f86",
+  "priced_message_count": 0,
+  "total_cost_micros": 0,
+  "unpriced_messages_having_usage_count": 0
+}
+```
+
+### Responses
+
+| Status | Meaning                                                 | Description | Schema                                           |
+|--------|---------------------------------------------------------|-------------|--------------------------------------------------|
+| 200    | [OK](https://tools.ietf.org/html/rfc7231#section-6.3.1) | OK          | [codersdk.ChatCost](schemas.md#codersdkchatcost) |
+
+To perform this operation, you must be authenticated. [Learn more](authentication.md).
+
 ## Get chat diff contents
 
 ### Code samples

docs/reference/api/schemas.md

@@ -2517,6 +2517,26 @@ AuthorizationObject can represent a "set" of objects, such as: all workspaces in
 | `description` | string | false    |              | Description is the tool's human-readable summary; may be empty.                                                   |
 | `name`        | string | false    |              | Name is the tool name with the "<server>__" prefix the agent adds stripped, so it reads as the server exposes it. |
 
+## codersdk.ChatCost
+
+```json
+{
+  "chat_id": "efc9fe20-a1e5-4a8c-9c48-f1b30c1e4f86",
+  "priced_message_count": 0,
+  "total_cost_micros": 0,
+  "unpriced_messages_having_usage_count": 0
+}
+```
+
+### Properties
+
+| Name                                   | Type    | Required | Restrictions | Description |
+|----------------------------------------|---------|----------|--------------|-------------|
+| `chat_id`                              | string  | false    |              |             |
+| `priced_message_count`                 | integer | false    |              |             |
+| `total_cost_micros`                    | integer | false    |              |             |
+| `unpriced_messages_having_usage_count` | integer | false    |              |             |
+
 ## codersdk.ChatDiffContents
 
 ```json