The budget test imported the startup gate but hand-copied the daemon client's
connect and request timeouts, because those were module-private. Raising
REQUEST_TIMEOUT_MS in main would then leave the watchdog silently short and the
test still green — the drift it exists to catch.
Move the three to an import-free module both sides can read, and note in each
pinned file that it is typechecked under the web config so it stays that way.