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)

coderd/database/dbmetrics/querymetrics.go

@@ -152,6 +152,14 @@ func (m queryMetricsStore) AllUserIDs(ctx context.Context, includeSystem bool) (
 	return r0, r1
 }
 
+func (m queryMetricsStore) ArchiveChatByID(ctx context.Context, id uuid.UUID) error {
+	start := time.Now()
+	r0 := m.s.ArchiveChatByID(ctx, id)
+	m.queryLatencies.WithLabelValues("ArchiveChatByID").Observe(time.Since(start).Seconds())
+	m.queryCounts.WithLabelValues(httpmw.ExtractHTTPRoute(ctx), httpmw.ExtractHTTPMethod(ctx), "ArchiveChatByID").Inc()
+	return r0
+}
+
 func (m queryMetricsStore) ArchiveUnusedTemplateVersions(ctx context.Context, arg database.ArchiveUnusedTemplateVersionsParams) ([]uuid.UUID, error) {
 	start := time.Now()
 	r0, r1 := m.s.ArchiveUnusedTemplateVersions(ctx, arg)
@@ -352,14 +360,6 @@ func (m queryMetricsStore) DeleteApplicationConnectAPIKeysByUserID(ctx context.C
 	return r0
 }
 
-func (m queryMetricsStore) DeleteChatByID(ctx context.Context, id uuid.UUID) error {
-	start := time.Now()
-	r0 := m.s.DeleteChatByID(ctx, id)
-	m.queryLatencies.WithLabelValues("DeleteChatByID").Observe(time.Since(start).Seconds())
-	m.queryCounts.WithLabelValues(httpmw.ExtractHTTPRoute(ctx), httpmw.ExtractHTTPMethod(ctx), "DeleteChatByID").Inc()
-	return r0
-}
-
 func (m queryMetricsStore) DeleteChatMessagesAfterID(ctx context.Context, arg database.DeleteChatMessagesAfterIDParams) error {
 	start := time.Now()
 	r0 := m.s.DeleteChatMessagesAfterID(ctx, arg)
@@ -3663,6 +3663,14 @@ func (m queryMetricsStore) TryAcquireLock(ctx context.Context, pgTryAdvisoryXact
 	return r0, r1
 }
 
+func (m queryMetricsStore) UnarchiveChatByID(ctx context.Context, id uuid.UUID) error {
+	start := time.Now()
+	r0 := m.s.UnarchiveChatByID(ctx, id)
+	m.queryLatencies.WithLabelValues("UnarchiveChatByID").Observe(time.Since(start).Seconds())
+	m.queryCounts.WithLabelValues(httpmw.ExtractHTTPRoute(ctx), httpmw.ExtractHTTPMethod(ctx), "UnarchiveChatByID").Inc()
+	return r0
+}
+
 func (m queryMetricsStore) UnarchiveTemplateVersion(ctx context.Context, arg database.UnarchiveTemplateVersionParams) error {
 	start := time.Now()
 	r0 := m.s.UnarchiveTemplateVersion(ctx, arg)