FN-5884: preserve quick chat session across reopens

Keep quick chat warm and restore the last opened conversation per project.

- persist the active quick chat session id in per-project local storage and restore it before falling back to latest activity
- retain in-memory quick chat state across close/reopen while resetting chat state correctly when the project changes
- add storage, hook, and FAB coverage for restored sessions, warm reopen behavior, and project switching; document the updated quick chat behavior

Files changed:
 docs/dashboard-guide.md                            |   3 +-
 packages/dashboard/app/components/QuickChatFAB.tsx |  29 ++++--
 .../app/components/__tests__/QuickChatFAB.test.tsx | 112 +++++++++++++++++++--
 .../__tests__/quickChatLastSessionStorage.test.ts  |  55 ++++++++++
 .../app/hooks/__tests__/useQuickChat.test.ts       |  70 +++++++++++++
 .../app/hooks/quickChatLastSessionStorage.ts       |  41 ++++++++
 packages/dashboard/app/hooks/useQuickChat.ts       |  25 +++++
 7 files changed, 319 insertions(+), 16 deletions(-)

Fusion-Task-Id: FN-5884

Fusion-Task-Lineage: 4d689611-1824-41db-8fc2-d543407316ff

docs/dashboard-guide.md

@@ -189,7 +189,8 @@ Quick Chat is an optional floating panel for fast, project-scoped assistant conv
 - Entering `/new` or `/clear` (exact match after trimming) in the Quick Chat composer clears the active thread target: direct/model targets use `startFreshSession(...)`, while room targets call `rooms.clearRoom(activeRoom.id)`.
 - The `+` action opens an inline new-session chooser (inside the panel, not a modal) with `Model` selected by default and optional switch to `Agent`
 - Submitting the inline chooser uses explicit fresh-session creation and immediately persists/selects the new thread, then refreshes the session dropdown list
-- On every open, Quick Chat restores the most recently used non-archived session by latest activity (`max(lastMessageAt, updatedAt)`); only when no prior session exists does it fall back to the first agent / configured default model.
+- On first open for a project, Quick Chat restores the last opened non-archived session from per-project local storage; if that saved session is missing, it falls back to the most recently touched non-archived session by latest activity (`max(lastMessageAt, updatedAt)`), and only falls back to the first agent / configured default model when no prior session exists.
+- Closing and reopening Quick Chat keeps the active conversation warm in memory, so messages stay visible without a conversation reload or "Loading conversation…" flash.
 - Queued follow-up messages entered while a Quick Chat response is still streaming now persist per session, so closing/reopening the panel restores the queued text and flushes it once the active response completes.
 - Resume lookups still use targeted session queries instead of loading the full active-session list first
 - Tool-call summaries in the floating quick-chat panel are intentionally condensed into a single-line header row (especially on small screens) so tool name + status stay scannable without multi-line wrapping