fix(server): StartHTTPServer shutdown does not wait for background DB init #664

Found by the independent re-review of #646 at 574caf4.

StartHTTPServer (internal/server/http.go:162-186) starts the background initializer with app.startBackgroundInit(sigCtx) (http.go:113) but never waits for it. On SIGTERM it runs server.Shutdown, returns nil, and cmd/server/main.go:52 runs defer app.Close() while ensureDB may still be running.

Effects (not fatal; Close still runs):

• app.Close() (internal/server/app.go:949) reads app.DB without a lock while ensureDB may be writing it. That is a data race, and a pool created just after Close read nil is never closed.
• runMigrationsBounded takes a pool, not a context, so SIGTERM mid-migration is not interrupted; the process exit kills it mid-run.

Fix sketch: make startBackgroundInit return a channel closed when initializeUntilReady exits, and have StartHTTPServer wait on it after server.Shutdown, inside the same 30s shutdownCtx. A draft with a test (TestRunUntilReadyClosesDoneAfterInitializerExits) passes locally: ~/.claude/agent-comms/messages/draft-20261008-646-f4-shutdown-wait.patch.

Deferred out of #646 by the fleet lead; to be done as a follow-up PR after #646 merges.