feat(site/src/pages/AgentsPage/components): drag chats onto project folders in the sidebar - #30795

PATCH /api/v2/chats/{chat} now accepts project_id. A UUID moves an idle
root chat into a project of its owner and organization; uuid.Nil removes
it from its project. The project checks are the ones of chat creation,
now shared by validateChatProjectSelection.

The chatstate machine gains a SetProject transition, allowed only from
W, E0 and E1. SetFamilyProject locks the root first and then each
subagent chat, so a busy family returns 409 and the move never overlaps
a step. chatd publishes a project_change watch event for each family
member after the commit.

…ed chat in the cache, not the DOM

FE1 leaves rendered presence to screenshots. The row menu test now checks
the move request and the project page's own list cache, and the new
ChatMovedToAnotherProject story shows that the page leaves out a cached
chat of another project.

… its project

A chat moved out of its project, or whose project was deleted, kept the
memory index the model saw there, while the memory tools were gone. A
root chat outside a project now has an empty index, so its next turn
start sends an update that removes those memories. Such a chat reads the
prompt only at turn start, the only step where that removal can be due.

… drags by name

dnd-kit's default announcements read the draggable and droppable IDs, so
a screen reader heard "move:<id>" and "project:<id>" during the new
keyboard drag. The sidebar's DndContext now announces the chat title and
the folder name, and pin drags keep the defaults.

…ithout Move to project in stories

The archived, shared and subagent menu cases asserted DOM absence in
Vitest, which the frontend contract (FE1) leaves to screenshots. Three
stories now open those menus with the chat-projects experiment on, and
the Vitest absence checks are removed.

…ove after the menu closes

The refused-move test waited for the menu item to leave the DOM before it
checked the toast. The update now rejects only after the select, so the
test still shows that the toast outlives the menu without a DOM check.

…ange

A move keeps the chat's updated_at, so the watch merge takes project_id
from each project_change payload in arrival order. The server publishes
after it releases the root lock, so two quick moves can reach another
tab in reverse order, and the open chat then kept the older project in
its top bar and Move menu. The list caches refetched on project_change;
the chat entity did not.

The watch handler now refetches the open chat on project_change. Each
event first cancels an entity refetch in flight, and the server
publishes after commit, so the refetch after the last event reads the
committed project. A first fetch still in flight restarts, because
invalidation would reuse a request that may predate the move.

The archive tests and the new move tests share one mock of the watch
socket.

…ojects

# Conflicts:
#	site/src/pages/AgentsPage/AgentsPageLayout.test.tsx

…the drop story reachable

…ojects

# Conflicts:
#	site/src/pages/AgentsPage/components/ChatsSidebar/ChatsSidebar.stories.tsx
#	site/src/pages/AgentsPage/components/ChatsSidebar/chats/ChatsPanel.tsx
#	site/src/pages/AgentsPage/components/ChatsSidebar/chats/ProjectFolders.test.tsx

This branch becomes the top layer of a stack. The merge takes the
lower layers, including their cleanups, and keeps this branch's
changes, so the PR diff is only the sidebar drag and drop.