I recommend you go through all control settings in the menu, if its only Destiny then its possible you've accidentally changed something when flicking through menus. Unlikely though.
Almost all controllers no matter how fancy use the same analogue switches and they are a lot more fragile than you'd like to think. They aren't expensive but you need some decent precision soldering skills to swap them out.
But sounds like you have more of an obstruction than a broken analogue switch clip, can you rotate the stick 360° freely? Or can you feel any bumps or grinding?
If you're confident with electronics I'd recommend you take it apart and clean it, you might have some dust or something built up around the NORTH axis clip on the analogue switch. Some compressed air or contact cleaner will help if you have them. Use cotton buds (Q-tips) or an old, soft toothbrush.
Also, look in the MS store (Xbox) for an app called Controller Tester (or summink like that) that allows you to see how your analogue sticks are being received.
Good luck.
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Thank you for the advice!