Stop working in a 'twilight zone'
As a company, a decision should be made: do you want to move towards an Agile way of working with Sprints and all other things it entails or do you want to adopt a more 'classical' approach?
If sprints are to be used, then the only people who can decide what work will be done in a sprint are the scrum team: the product owner and the developers. Note that there is no 'project manager' in this scenario. The product owner is the one who decides the priority of all the different stories and functionalities and then the scrum team decides during sprint planning which items they will pick up during that iteration. There is no room here for anyone to force the developers to take on more work. If the different project managers (who will become stakeholders in the new structure) want the priorities to change, they will need to convince the product owner to change the priorities. If during a sprint it turns out that the stories are all fully done (including testing) and there's room for more work, the scrum team will have a quick meeting to decide which stories they will take into the sprint in addition to the stories that were decided on during the sprint planning. If multiple stakeholders have conflicting priorities, the product owner should have a meeting with all of them and have them decide together what they think the priorities should be, of which they can then attempt to convince the product owner.
In a more classical approach, something similar should happen. Since the project managers are not the ones doing the work, they should leave the judgement of what can be done within a given timeframe to the experts: the tech leads. They can always ask for more, but should trust the judgement of the tech leads. If multiple project managers depend on the same set of people to get their tasks done, those project managers should decide between themselves what the order of priority in the tasks should be and then trust the tech leads to ensure that this order is respected. In this case there's no such thing as a 'stretch goal': the work gets completed in order of priority and if someone happens to run out of tasks they will go up the proverbial foodchain to ask what their next task should be.
By trying to work in the classical way within an Agile/Scrum structure of sprints, an incredible amount of pressure is created on the developers, which is practically always counterproductive. In such a classical structure, it should never be up to the developer to decide whether they should be working on a task for one project manager or the other, since they are unable to correctly assess which task has the most business value. The way of working that seems to be described in the question here will lead to developer burnout, which leads to developers leaving for greener pastures.