Manager is a useless low-level job, however, good managers exists and you will probably won't see one in most firms. Real manager is a high position which requires years of coding experience as well as at least basic cross-domain experience in fields like design, business development, operations, sales, marketing. So it explains why it's much harder to find a good engineering manager then a good engineer and why most of managers are "kids"/"freshies" who often put themselves in a such laughful situation like described one in the question.
Anyway, each professional should master self-management and teamwork skills on a personal basis.
The problem of other team in that case is only problem of that team and the only who should be fired, are them. However, if any of your teams in organization is using old technology or any tools inefficiently, it is yours, engineers, responsibility to propose changes, in any case it is mostly the responsibility of the CTO/VP of Engineering/Lead Engineer/etc.
There is no my team, their team, there is no I, they, there is only WE and OUR ORGANIZATION and if part of that organization suffers, the whole organization suffers, but again if the Business Operations in that organization are not well established or not transparent/known enough, then cross-team/department work can't be efficient and one team won't be able to help another. This is the responsibility of COO or CEO, while most companies, especially, smaller ones and those "design/dev agencies" don't have real executive officers.
Instead of just laughing in your situation, I would at least propose a solution which could be an implementation of the own tool/back-office/panel/whatever or use of the any 3rd party ready solution.
Answering your direct question I don't have managers and will never have typical management system in my organization. As I said anyone MUST master management skills, it's part of your "professional" definition, which includes self-management, self-control, proper communication (including cross-team/department), awareness, proposal of solutions and ACTING on your own without waiting for permission, orders, tasks, confirmations.
So the only manager for me is myself and this one manager is still not satisfying me enough, however, talking from the perspective of people under my leadership, I always try to be a Leader not a Manager and there is a huge difference between both, but in any case one person may help another even if it's not your direct skillet or job.
Anyone must work, adapt or die.