Short term: Mentally check out. Embrace the Zen of just doing what's asked of you. It's not your job to be a go-getter anymore. Half because of institutional complexity/inertia, and half because in a tall organization hierarchy the middle managers don't want anyone below them swimming outside their lane (even if it would be to their unit's benefit and they can take every ounce of credit).
Or, more usefully, find (or ask your management to help you find) something else useful to do while you're waiting on the other team.
Or, more usefully, find (or ask your management to help you find) something else useful to do while you're waiting on the other team.