feat(server,web): DB-served session list, CLI-session visibility toggle, and sidebar group paging (#158)

Co-authored-by: Claude Fable 5 <noreply@anthropic.com>

packages/server/src/db/schema.ts

@@ -4,7 +4,10 @@
  * SQLite stores only indexes and aggregates: users / login sessions / Project authorization /
  * Agent & Session indexes / usage summaries / error records / UI preferences. Agent State,
  * Trace, and Workspace still follow the local directory-based storage rules.
- * Product not yet released: no migration branches — everything is CREATE IF NOT EXISTS, formed once.
+ * Product not yet released: no migration branches — everything is CREATE IF NOT EXISTS, formed
+ * once. The one exception: columns added to an existing table after release of a web.db are
+ * ALTERed in by the idempotent per-column guard in database.ts (ensureColumn), since CREATE
+ * TABLE IF NOT EXISTS never touches an existing table.
  */
 
 export const SCHEMA_SQL = `
@@ -48,8 +51,11 @@ CREATE TABLE IF NOT EXISTS sessions (
   approval_mode TEXT NOT NULL DEFAULT 'allow-all',   -- allow-all|deny-all|read-only|always-ask
   title         TEXT,                                -- auto-generated by the model after the first exchange; NULL=not yet (frontend shows "New chat")
   archived_at   TEXT,                                -- archive time; NULL=not archived (shown by default; archived ones move under "Archived")
+  client        TEXT,                                -- creating client: 'web' (created via the Web App) | 'cli' (adopted from a CLI Trace); NULL = legacy row, treated as web
+  has_trace     INTEGER NOT NULL DEFAULT 0,          -- cache: a Trace record exists (set at task start / adoption / subagent registration; lazily backfilled by list hydration)
   created_at    TEXT NOT NULL
-);                                            -- session origin is NOT stored: session_meta in the Trace is the single source of truth (see runtime/session-sources.ts)
+);                                            -- the schedule/subagent SOURCE is NOT stored: session_meta in the Trace is the single source of truth (see runtime/session-sources.ts); "client" is a different, DB-only axis (who created the row)
+CREATE INDEX IF NOT EXISTS idx_sessions_agent_created ON sessions(project_id, agent_id, created_at DESC);
 CREATE TABLE IF NOT EXISTS usage_records (
   id                INTEGER PRIMARY KEY AUTOINCREMENT,
   ts                TEXT NOT NULL,