Add Databases management page and roadmap coverage audit

/databases page (new nav item): expandable managed-DB cards with
connection URL + copy, start/stop/restart actions, metrics summary, and
backup list with create/restore. Verified e2e against a real postgres:16
container — provision, psql connect, stop/start, seed, 6.4MB backup,
drop, restore with data recovered.

ROADMAP: marked databases/cron/git-connect/agents done with evidence,
corrected stale inventory rows (frontend now consumes 52 API ops),
added uncovered items — GitHub App install surfacing, database→service
binding, backup export + scheduled backups, service exec console,
OAuth e2e w/ real creds, remaining sqlc port, demo-data parity.

Generated with [Devin](https://devin.ai)

Co-Authored-By: Devin <158243242+devin-ai-integration[bot]@users.noreply.github.com>

app/frontend/src/lib/api-client.ts

@@ -1277,6 +1277,37 @@ export async function listGitBranches(
 
 export type CreateDatabaseInput = components['schemas']['CreateDatabaseRequest'];
 export type DatabaseEntity = components['schemas']['Database'];
+export type DatabaseBackupEntity = components['schemas']['DatabaseBackup'];
+
+export async function listDatabases(): Promise<DatabaseEntity[]> {
+  const payload = await requestJson<{ databases?: DatabaseEntity[] }>('/databases');
+  return payload.databases ?? [];
+}
+
+export async function getDatabase(id: string): Promise<DatabaseEntity> {
+  return requestJson<DatabaseEntity>(`/databases/${encodeURIComponent(id)}`);
+}
+
+export async function databaseAction(id: string, action: 'start' | 'stop' | 'restart'): Promise<void> {
+  await requestJson(`/databases/${encodeURIComponent(id)}/action`, {
+    method: 'POST',
+    body: JSON.stringify({ action }),
+  });
+}
+
+export async function createDatabaseBackup(id: string): Promise<void> {
+  await requestJson(`/databases/${encodeURIComponent(id)}/backup`, {
+    method: 'POST',
+    body: JSON.stringify({ database_id: id }),
+  });
+}
+
+export async function restoreDatabaseBackup(id: string, backupId: string): Promise<void> {
+  await requestJson(`/databases/${encodeURIComponent(id)}/restore`, {
+    method: 'POST',
+    body: JSON.stringify({ database_id: id, backup_id: backupId }),
+  });
+}
 
 export async function createManagedDatabase(
   input: CreateDatabaseInput,