Hi! I totally understand, it's such a tough phase, but the good news is this is actually really normal and peaks right around her age. Nine months is when separation anxiety tends to hit hardest, so what you're seeing isn't unusual at all, and most babies do work through it as they get older and understand object permanence better.
That said, a few things can help ease it: keeping drop-offs as consistent as possible (same time, same routine) seems to help a lot, the predictability makes it less scary for them. And since she clearly bonds well with her favourite teacher, it might be worth having that teacher do the handover each time if the school can swing it; some mums have found that makes a real difference. The fact that she's been settling at school since four months old is actually a positive sign, she knows the place, she just needs reassurance right now that you're coming back.
The clinging phase usually does ease up over the next few months as she gets older and her understanding develops, but every baby moves at their own pace. It's worth checking in with her paediatrician too, just to make sure there's nothing else going on and to get their take on what might help her specifically.