fix(tui): close SQLite stores deterministically so Windows can delete t.TempDir

[aheritier]

🤖 Automated architect agent — this comment was posted by the architect bot from Docker Agentic Platform, not by a human engineer

Problem

windows-tests flakes (~6 % of ci runs over the last 100) with, in 3 of the 6 Windows-only failures:

--- FAIL: TestBackgroundAgent_PerAgentContextInSidebar (2.65s)
    testing.go:1617: TempDir RemoveAll cleanup: unlinkat C:\...\Temp\...\data\tui_state.db:
    The process cannot access the file because it is being used by another process.

(also session.db in TestChat_DegenerateResizeDoesNotPanic). Runs: 34329154242, 34194019096, 34325172091.

Windows refuses to delete a file with an open handle; Go's t.TempDir() cleanup retries sharing violations for only 2 s. Two SQLite handles in the tuitest-driven e2e/tui tests outlived that window:

• tui_state.db is closed only by the detached goroutine armed in contextShutdownCmd (<-ctx.Done(); cleanupManagedResources()), which nothing joins. tuitest's cleanup quits the program but never releases the model's resources, so a WAL checkpoint + fsync on a slow runner races t.TempDir. In-package unit tests already work around this with t.Cleanup(m.cleanupManagedResources); the external e2e/tui package couldn't.
• session.db: sql.DB.Close() only closes idle connections. One checked out by an in-flight persistence write (token usage / title, on the runtime observer goroutine) is released after Close returned — the Failed to persist token usage … sql: database is closed warnings in the logs are the same writers landing a moment later.

Fix

• sqliteutil.CloseDB(db): Close() then wait (bounded, 5 s) until db.Stats().OpenConnections == 0. Used by tuistate.Store.Close. session.SQLiteSessionStore.Close gets the same database/sql-only drain inline, because pkg/session must stay free of the SQLite driver (e2e/dependencies_test.go; see pkg/session/sqlitestore).
• appModel.Shutdown() (exported, wraps the sync.Once-guarded cleanupManagedResources); tuitest.New calls it right after the program stops when the model implements it — same optional-interface pattern as SetProgram.

Result: every driver-based test closes tui_state.db synchronously before rt.Close, store.Close and t.TempDir run, and store closes don't return until the file handle is gone.

Validation

• go build ./..., golangci-lint run on touched packages: clean
• go test ./pkg/sqliteutil/... ./pkg/session/... ./pkg/tui/... ./e2e/tui/... ./pkg/app/... ./pkg/runtime/ ./cmd/root/: pass (Linux)
• New tests: TestCloseDB_WaitsForInFlightConnection, TestCloseDB_IdleReturnsImmediately, TestSQLiteSessionStore_CloseWaitsForInFlightConnection, TestDriver_CleanupShutsDownModelAfterProgramStops
• Windows: cannot be exercised locally; the windows-tests job on this PR is the check.

Not in this PR

The other 3 Windows-only flakes are timing budgets (PowerShell start-up under load: pkg/hooks TestExecuteStop, backgroundjobs recall test; pkg/userconfig 5 s lock timeout falling back to unlocked writes). Diagnosis and a prioritized plan for those are in the linked task report.