fix: normalize project session payloads

The sidebar had to understand cursorSessions, codexSessions,
and other provider buckets because /api/projects exposed
provider-shaped arrays.

That leaked backend adapter storage into project state and made
frontend behavior drift each time a provider needed another bucket
or exception.

Return one sessions list with provider metadata instead. Project
state, search, and running-session filtering now share one contract,
while provider-specific storage remains behind the backend boundary.

src/types/app.ts

@@ -29,6 +29,7 @@ export interface ProjectSession {
   updated_at?: string;
   lastActivity?: string;
   messageCount?: number;
+  provider?: LLMProvider;
   __provider?: LLMProvider;
   // Tags the session with the owning project's DB `projectId` so UI handlers
   // (session switching, sidebar focus, etc.) can match against selectedProject.
@@ -60,10 +61,6 @@ export interface Project {
   path?: string;
   isStarred?: boolean;
   sessions?: ProjectSession[];
-  cursorSessions?: ProjectSession[];
-  codexSessions?: ProjectSession[];
-  geminiSessions?: ProjectSession[];
-  opencodeSessions?: ProjectSession[];
   sessionMeta?: ProjectSessionMeta;
   taskmaster?: ProjectTaskmasterInfo;
   [key: string]: unknown;