feat(chats): archive chats instead of hard-deleting them (#22406)

## Summary

The UI has always labeled the action as "Archive agent" but the backend
was performing a hard `DELETE`, permanently destroying chats and all
their messages.

This change replaces the hard delete with a soft archive, consistent
with the pattern used by template versions.

## Changes

### Database
- **Migration 000423**: Add `archived boolean DEFAULT false NOT NULL`
column to `chats` table
- Replace `DeleteChatByID` query with `ArchiveChatByID` (`UPDATE SET
archived = true`)
- Add `UnarchiveChatByID` query (`UPDATE SET archived = false`)
- Filter archived chats from `GetChatsByOwnerID` (`WHERE archived =
false`)

### API
- Remove `DELETE /api/experimental/chats/{chat}`
- Add `POST /api/experimental/chats/{chat}/archive` — archives a chat
and all its descendants
- Add `POST /api/experimental/chats/{chat}/unarchive` — unarchives a
single chat (API only, no UI yet)

### Backend
- `archiveChatTree()` recursively archives child chats (replaces
`deleteChatTree()` which hard-deleted)
- Chat daemon's `ArchiveChat()` archives the full chat tree in a
transaction
- Authorization uses `ActionUpdate` instead of `ActionDelete`

### SDK
- Replace `DeleteChat()` with `ArchiveChat()` and `UnarchiveChat()`
- Add `Archived` field to `Chat` struct

### Frontend
- `archiveChat` API call uses `POST .../archive` instead of `DELETE`
- No UI changes — the "Archive agent" button now actually archives
instead of deleting

## Design Decision

This follows the **template version archive pattern** (Pattern B in the
codebase):
- `archived boolean` column (not `deleted boolean`)
- Dedicated `POST .../archive` and `POST .../unarchive` routes (not
repurposing `DELETE`)
- Reversible — users can unarchive via the API (UI for this will come
later)

docs/reference/api/chats.md

@@ -0,0 +1,37 @@
+# Chats
+
+## Archive a chat
+
+### Code samples
+
+```shell
+# Example request using curl
+curl -X POST http://coder-server:8080/api/v2/chats/{chat}/archive
+
+```
+
+`POST /chats/{chat}/archive`
+
+### Responses
+
+| Status | Meaning                                                         | Description | Schema |
+|--------|-----------------------------------------------------------------|-------------|--------|
+| 204    | [No Content](https://tools.ietf.org/html/rfc7231#section-6.3.5) | No Content  |        |
+
+## Unarchive a chat
+
+### Code samples
+
+```shell
+# Example request using curl
+curl -X POST http://coder-server:8080/api/v2/chats/{chat}/unarchive
+
+```
+
+`POST /chats/{chat}/unarchive`
+
+### Responses
+
+| Status | Meaning                                                         | Description | Schema |
+|--------|-----------------------------------------------------------------|-------------|--------|
+| 204    | [No Content](https://tools.ietf.org/html/rfc7231#section-6.3.5) | No Content  |        |