refactor(session-search): move the AI Vault project key to shared

The host must spell a project key exactly as the client does, so the two
sides share one function instead of two copies that can drift.

src/renderer/src/components/right-sidebar/ai-vault-project-key.ts

@@ -1,18 +1,9 @@
 import type { ProjectHostSetup } from '../../../../shared/project-types'
 import type { Repo } from '../../../../shared/repo-types'
 import type { Worktree } from '../../../../shared/worktree/types'
+import { toAiVaultProjectKey } from '../../../../shared/ai-vault-project-key'
 
-export function toAiVaultProjectKey(
-  projectId: string | null | undefined,
-  repoId?: string | null
-): string | null {
-  if (projectId) {
-    // Why: legacy projections can already use repo-prefixed project ids; wrapping
-    // them again would split active scope and resolved session keys.
-    return projectId.startsWith('repo:') ? projectId : `project:${projectId}`
-  }
-  return repoId ? `repo:${repoId}` : null
-}
+export { toAiVaultProjectKey } from '../../../../shared/ai-vault-project-key'
 
 export function resolveActiveProjectKey(
   activeRepo: Repo | null,

src/renderer/src/components/right-sidebar/ai-vault-scope-paths.ts

@@ -6,6 +6,7 @@ import type { ProjectHostSetupProjection } from '../../../../shared/project-host
 import type { ProjectHostSetup } from '../../../../shared/project-types'
 import type { Worktree } from '../../../../shared/worktree/types'
 import { splitWorktreeIdForFilesystem } from '../../../../shared/worktree/id'
+import { toAiVaultProjectKey } from '../../../../shared/ai-vault-project-key'
 
 export function deriveAiVaultWorkspaceScopePaths(
   activeWorktree: Pick<Worktree, 'id' | 'path' | 'priorWorktreeIds' | 'repoId'> | null,
@@ -103,11 +104,7 @@ function worktreeProjectKey(
   entry: Pick<Worktree, 'projectId' | 'repoId'> | { projectId?: string | null; repoId?: string },
   setup?: { projectId?: string | null; repoId?: string }
 ): string | null {
-  const projectId = entry.projectId ?? setup?.projectId ?? null
-  if (projectId) {
-    return projectId.startsWith('repo:') ? projectId : `project:${projectId}`
-  }
-  return entry.repoId ? `repo:${entry.repoId}` : null
+  return toAiVaultProjectKey(entry.projectId ?? setup?.projectId ?? null, entry.repoId)
 }
 
 /**

src/shared/ai-vault-project-key.ts

@@ -0,0 +1,16 @@
+/**
+ * One spelling of "which project" for the sessions panel and for a host
+ * resolving a search scope, so a key minted on a client and a key matched on the
+ * execution host cannot drift apart.
+ */
+export function toAiVaultProjectKey(
+  projectId: string | null | undefined,
+  repoId?: string | null
+): string | null {
+  if (projectId) {
+    // Why: legacy projections can already use repo-prefixed project ids; wrapping
+    // them again would split active scope and resolved session keys.
+    return projectId.startsWith('repo:') ? projectId : `project:${projectId}`
+  }
+  return repoId ? `repo:${repoId}` : null
+}