fix(sidebar): search the managed chats along with project sessions (#3212)

* fix(sidebar): search the managed chats along with project sessions

The sidebar builds search data per group, and every group renders
`filteredNodes ?? []` while a query is active. Only project groups were ever
given that data, so the managed chats — which render outside any project
section — collapsed to an empty list as soon as anything was typed, however
well a title matched. The header count ignored them for the same reason.

Pass the chats group to the sections hook as a standalone group so it takes
the same search pass and joins the match count. Building it before the hook
runs keeps search-data ownership in one place instead of registering entries
from the rendering component.

No CHANGELOG entry: it is left out deliberately to keep this branch free of
conflicts with other open PRs, and is to be written at release time.

fixes #3200

* fix(sidebar): report the real search match count to the header

The header rendered whatever `SessionSidebar` passed it, and that was a
literal `0` — so "0 matches" was shown no matter how many sessions matched.
The count exists: the sections hook already computes it, but only the session
list can see it, and the header renders above the list.

Report it upwards from the list instead of recomputing it in the header, so
the number and the visible rows cannot disagree, and reset it to 0 when the
list unmounts.

fixes #3200

* fix(sidebar): keep chat-only search results on screen

The chats render inside the scroller's top content, and the branch that
handles "no project section matched" replaced the whole list with the empty
state. A query matching only a chat therefore showed "No matching sessions"
while the header — now reporting the real count — said one match, and the
chat itself stayed hidden. That is the exact reproduction in the issue; the
earlier manual check missed it because the query used also matched a project
session.

Tell the scroller when its top content holds results, and keep it on screen
in that branch. The decision moves to `sessionProjectRender` next to the
other render-selection helpers, where it can be tested without mounting the
Vite-only component graph.

fixes #3200

packages/ui/src/components/session/SessionSidebar.tsx

@@ -77,6 +77,8 @@ const SessionSidebarComponent: React.FC<SessionSidebarProps> = ({
   const { t } = useI18n();
   const [isSessionSearchOpen, setIsSessionSearchOpen] = React.useState(false);
   const [sessionSearchQuery, setSessionSearchQuery] = React.useState('');
+  // Reported by the session list below: the header cannot see what matched.
+  const [searchMatchCount, setSearchMatchCount] = React.useState(0);
   const sessionSearchContainerRef = React.useRef<HTMLDivElement | null>(null);
   const sessionSearchInputRef = React.useRef<HTMLInputElement | null>(null);
   const [editingProjectDialogId, setEditingProjectDialogId] = React.useState<string | null>(null);
@@ -631,7 +633,7 @@ const SessionSidebarComponent: React.FC<SessionSidebarProps> = ({
         sessionSearchQuery={sessionSearchQuery}
         setSessionSearchQuery={setSessionSearchQuery}
         hasSessionSearchQuery={hasSessionSearchQuery}
-        searchMatchCount={0}
+        searchMatchCount={searchMatchCount}
         collapseAllProjects={projectView.actions.collapseAllProjects}
         expandAllProjects={projectView.actions.expandAllProjects}
       />
@@ -668,6 +670,7 @@ const SessionSidebarComponent: React.FC<SessionSidebarProps> = ({
           isWorktreeTopologyLoading,
           unresolvedWorktreeProjectPaths,
           projectView: projectView.state,
+          onSearchMatchCountChange: setSearchMatchCount,
         }}
         actions={{
           rowActions: {