I agree with all of what you said. I think the miscommunication here is the obvious root problem: they both have assumptions about the other that are not cleared up for now because they don't have an open discussion about it. It is clear that Shuraka respects Tei a great deal, but he doesn't know him; beside the fact a dozen years have passed since they last saw each other, he never tries to put himself in his shoes, starting by understanding his culture and where he comes from, and what it means for a man like him to find himself in this kind of situation. It is obviously linked to the way the fight for the throne happened and the way he was raised at the Padisha, but as long as Shuraka fails to try to really understand Tei, they will keep going in circles and the misunderstanding and anguish will deepen.
Now as for Tei, I think his biggest mistake is never asking questions. It is clear that even though he is "beneath" Shuraka when it comes to hierarchy, there are little to no chance that Shuraka wouldn't answer his questions about his standing here, his role, and what he's supposed to do (beside "stay by his side" of course), because even if Shuraka thinks Tei shouldn't bother with anything he considers would be a burden for him, he has every reason for Tei to know which position he holds in terms of power, only just to protect himself when Shuraka isn't around. I think it will be addressed soon because it's usually an important plot point, and we'll see how it goes.