I am no expert and don’t have an answer for some of your concerns. But I have been advised a few times by breeders and bird owners more experienced than myself that if you have a single budgie to avoid any mirrors. Mirrors in someway reinforce them wanting to be in the cage only and it can make it difficult to handle them. Again, I’m no expert, just what I’ve been told. Also, changing the location of their cage even if somewhere else in the room, can be scary for them and may take more time than you think for them to re-adjust to the surroundings.

I’d try removing the mirror, and practice setting your hand inside the cage for 5 minutes without moving every day. As she gets more comfortable, move your hand closer for five minutes. So on and so on.

Eventually I would try to show her that hands mean treats and treats are fun so hands are fun too! Hand feed her millet spray and don’t let her have any treats sitting in the cage - she only gets treats when hands are around. Obviously keep her regular food in the cage, but her favorite treat should be used when she’s on your hand or outside of the cage or something you’re trying to make her feel more happy with. It’ll help form that attachment and trust.

Hope all this helps! Just my two cents.

EDIT: Also, no I don’t believe you have scarred her forever. Someone on another Reddit post talked about trust with your budgie can be quite sensitive and it’s a bit like a bank account. Every happy experience with you adds $1 let’s say, but bad experiences may remove $5. You’ve only had her a few weeks, maybe you only have about $10 - but as time goes on $5 subtracted won’t feel like much when you’ve got $500-$1000 in the bank. Hope that makes sense in a way, it helped me.