Try turning cross platform matchmaking off before going to the Tower. And turn it back on when you're back in orbit. That helps me a lot on PS5. Went from anywhere between 2 to 5 minutes loading time to about 30 seconds. Easy on PS5 since the option's in the menu. Haven't tried it on Xbox yet.
Hope that helps.
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You need to restart the game to get any changes to crossplay to take effect on Xbox.
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I just load into the annex now, no issues with that spawn point for some reason