They can push whatever is staged for your car. If the new update is staged for your car, they can push that. If that was the case though, it would be showing up for you to download. All you are doing now is wasting your time, and service center people time.
"Stuck" is 8+ weeks. You are not stuck.
This is all entirely true, but I support new owners wasting service center's time, just to add to the feedback loop inside Tesla about how bad their communication is around software updates.
One lean manufacturing principal I really see value in is making problems visible, so they are detected and solved. Service tickets about old software are for sure tracked, and their labor cost on a priority list on some spreadsheet.
A simple readiness level chart of new updates, showing confidence level of Tesla that a particular update is validated in early testing and ready for wide adoption could solve a lot of the confusion about new updates.
They already have this data, as you can see it on the rates of roll out. When an update is ready for wide adoption (in Tesla's judgement) it spikes up above 50-55% of fleet installs in a day and a half. Prior to that they roll out tentatively at about 15% off fleet and stall, obviously waiting for feedback.
No 36 branch has gone above 30% without being superseded by a 36 dot update very suddenly. Personally, I try to hold off on any update until it goes over 10k installs on Teslafi, about 55 % of fleet. I've missed all serious problems with new updates this year.