Earlier quoted context omitted.
Start by actually talking to your management instead of just trying to be a rock star. "Hey, I'm spending a lot of time doing Team X's job and it's impacting on my assigned work, if you want me to keep doing this then put me in charge of Team X, otherwise let's all sit down together and clarify who is responsible for what."
So I'm asking this not to move the goalposts, but because it's the situation I'm in - what do if your manager is too weak/distracted/uncaring to actually act on this information and/or the projects in wait state on you are not actually within your manager's sphere of influence?
Of course, by the time you have upper management yelling at you because "several teams are waiting on you", the response becomes "why have you allowed several teams to become completely dependent on one overworked person?"
The other, more drastic solution (as someone else said) is simply to move jobs. This can be the only way to fix the issue if the entire management structure is corrupted and you don't think it's fixable from within. You could even just leave, start a consultancy company, and let the second team know that you're available for hire when they need you.