Subagent (child) chats could appear as standalone top-level
entries in the Agents sidebar when their parent chat fell
outside the loaded page set. `buildChatTree` promoted orphaned
children to root nodes because `GetChats` returned all chats
in a single flat, paginated list.

`GetChats` now returns only root chats (`parent_chat_id IS NULL`
is unconditional in the SQL). A new `GetChildChatsByParentIDs`
query fetches children for visible roots, and the handler
embeds them in each parent's `Children` field. The singular
`getChat` endpoint also embeds children for root chats. The
frontend `buildChatTree` reads children from the embedded field,
and WebSocket handlers route child events into the parent's
`children` array instead of prepending them at the top level.

`patchChat` enforces the archive-family invariant at the server:

- Archive on a child chat: rejected (400). `ArchiveChatByID`
  cascades at the root level only.
- Unarchive on a child chat: rejected (400) when the parent is
  still archived. Allowed when the parent is active so legacy
  lone-archived children can be recovered.

Gitsync's `MarkStale` broadcast path now uses
`GetChatsByWorkspaceIDs` directly instead of `GetChats` +
in-Go filter. `GetChats` is a single-purpose query for the
paginated sidebar.

`GetChildChatsByParentIDs` does not filter by archive state.
The cascade and the `patchChat` invariants keep child and
parent archive state consistent at write time; a read-time
filter would race those writes and could drop children whose
archive flag had not yet caught up with the parent's.

…r.UnarchiveChat

Replaces the standalone UnarchiveChildChatAtomic helper and the
handler's switch that bypassed chatDaemon with the archive path's
shape:

- Server.UnarchiveChat branches on ParentChatID.Valid internally.
  For a root chat it delegates to applyChatLifecycleTransition as
  before. For a child chat it opens an InTx that locks the child
  row (GetChatByIDForUpdate), re-reads the parent, rejects with
  ErrChildUnarchiveParentArchived if the parent is archived, and
  otherwise UnarchiveChatByID + publish events.
- patchChat's unarchive branch collapses to the same shape as
  archive: chatDaemon when available, plain UnarchiveChatByID
  fallback when not. No special-casing for child chats at the
  handler layer.
- ErrChildUnarchiveParentArchived remains exported so the handler
  can translate it to 400.
- Tests for the atomic path move from the deleted
  coderd/x/chatd/unarchive_test.go into TestUnarchiveChildChat
  against Server.UnarchiveChat, which is the supported path.

Behavior is unchanged (same invariant, same locking ordering,
same sentinel error). Code structure now matches Server.ArchiveChat
and does not introduce a second code path that skips chatDaemon.

Shortens the comments written in response to R8-R10 review feedback.
The why's are retained where they add context (one-way invariant,
child-lock-before-parent deadlock rationale, archived=false filter on
GetChatsByWorkspaceIDs). Removed are restatements of the code, future-
feature speculation, and self-justifications about what the tests\ndon't exercise.

Net -110 lines across the changed files; no behavior change.