I've been unable to post from Lightroom mobile to Instagram like I normally do. The 'Open in App' share option is missing in iOS 16. The 'share with app' option is useless; it doesn't allow me to scale or do any adjustments and sometimes cuts off the head in pictures (because there's no control).
We're having trouble reproducing your issue. Does it help if you sign out and back into Instagram, or perhaps re-install Instagram in case that helps it register as a share target on your device? Is LR the only app having trouble reaching IG?
I had the exact same issue when I upgraded to iOS 16 - I lost the 'open in app' option on the long press. Apparently it's a known issue. Ultimately I had to downgrade back to iOS 15 in order to regain the option. I'm not sure if it's an Adobe issue or an Apple issue. Either way it sucks.