feat(agents): persistent Lakebase thread store

[MarioCadenas]

What

Adds LakebaseThreadStore — a persistent ThreadStore for AppKit agents backed by Databricks Lakebase (Postgres). Today agents use InMemoryThreadStore, which loses every thread on restart and grows without bound; this closes that parity gap. The injection seam already existed (agents({ threadStore })), so this is one new store implementation plus lifecycle wiring — no plumbing surgery.

Implements the approved spec in design-docs/agent-persistent-threads-plan.md exactly.

How it works

• Raw parameterized pg SQL over a pool from createLakebasePool() (OAuth handled inside the pool). Not the DatabasePlugin data layer.
• Two user_id-scoped tables — agent_threads + agent_messages (FK ON DELETE CASCADE) — self-bootstrapped with CREATE TABLE IF NOT EXISTS on init() (once-guarded, select 1 connectivity probe first).
• Every query filters WHERE user_id = $ — the isolation boundary; a user can never read or mutate another user's threads.
• tool_calls stored as jsonb, preserving ToolCall.thoughtSignature verbatim (node-pg parses jsonb on read; JSON.stringify + ::jsonb cast on write). Date fields revived on read.
• Owns its pool by default (closed on shutdown); an injected pool is left alone.
• Optional init?()/close?() added to the ThreadStore interface (in-memory store untouched); wired into the agents plugin setup() (fail-fast) and shutdown().
• Optional postgres resource on the agents manifest (same field/env shape as the database plugin) so a deploy can bind Lakebase; unbound apps fall back to in-memory.

Commits

1. add persistent Lakebase thread store (schema + 5 methods) + unit tests
2. wire ThreadStore init/close lifecycle into agents plugin
3. optional postgres resource on agents manifest + export store
4. persistent threads example + docs

Verification (agent-run)

• New unit tests green (17 cases): per-method SQL + params, user_id scoping on every query, thoughtSignature round-trip, addMessage throws on missing thread, pool ownership, once-guarded bootstrap.
• pnpm -r typecheck clean (no new errors vs baseline).
• pnpm check:fix (oxlint + oxfmt) clean.
• pnpm build && pnpm docs:build succeed.
• Opt-in dev-playground example (agents({ threadStore: new LakebaseThreadStore() }) gated on LAKEBASE_ENDPOINT).

NOT verified

This has not been run against a live Lakebase. The SQL correctness (casts, CTE atomicity, jsonb round-trip, cascade) is only exercised against a mocked pool in unit tests. Live dogfood — deploy against a real Lakebase, create a thread, restart the app, confirm persistence and per-user scoping — is the remaining human step. Draft until then.

Deviations from the plan (flagged, not expanded)

• Commit scope appkit, not agents: commitlint's scope enum is [appkit, appkit-ui, shared, playground, docs, deps, release] — agents is rejected. PR title keeps (agents) per the task.
• Export via @databricks/appkit/beta, not the GA root index.ts: the agents plugin and the ThreadStore type are beta exports, so the store lives beside them ("beside the existing agents exports").
• Full postgres field set copied from the database manifest (host/databaseName/endpointPath/port/sslmode), not just the 5 named in the plan, so a bound deploy injects every env var createLakebasePool() reads.