I agree with BFNE that based on the further disclosures this sounds very fixable. Way too early to write the horse off because most horses will jump like this is you approach with an up and downing pong gait which in reality has no ability to carry them across the fence and then they do their best to get over. The horse is trying, bless her.
but that is exactly what I would expect. See what you have after a few months in the ring. Give her time.
A good bit of this fix requires a different ride from you or if in the chute encouragement to go forward. It is not wrong to use a stick behind your leg at takeoff on a horse that hangs. Not to beat it, mind you…leg on, a light tap and cluck to reinforce the forward aid and get the idea across. For many horses that will cure this entirely and get then jumping across. Lots of praise when then leap forward which many do in response to a tap on takeoff. Over a crossrail. Then GOOD GIRL!!! And lots of praise and pets. She will realize soon the effort felt better to her too. One of those, then just keep your leg on and cluck to her over the X. Same praise if she lands going forward. Etc.
When we say get her deep we mean jump nicely from the base, where all jumpers try to jump. Not a chip or a tight spot. you do not want to be taking long spots on horses with poor form, it encourages it and fliers are downright dangerous on a horse that hangs its Knees. That is classic horsemanship.
Many people consider those rampy Hunter oxers to be the bane of good form because they encourage flat jumping and drapey legs. Just read George Morris’ column regularly, he will note it. I have heard it from multiple sources. When I worked for a barn that did hunters we NEVER schooled those at home, only square oxers. Shows make the horses complacent enough. We used the kinda of exercises I described above. Pole, small square oxer, pole on landing side. Gymnastics. Bounces. Consistent canter to the base. Save the gap for shows. Gap enough and it takes your horse’s confidence away because that is fundamentally asking the horse to leave a bit long. Some horses we never did it on for that reason, the sensitive ones. Some horses can gap forever and not care but they are rarely the brilliant jumpers.
I personally would be jumping this horse over little tiny stuff a lot, like a few jumps every ride but no huge jump schools. Just add it in and make it seem boring and normal. Keep the number of total weekly efforts low, but expose her to jumps often. And tons and tons of trot and canter poles. I use that strategy with hot horses a fair bit and find it helps them a lot, but I am very good at just jumping 3-4 fences and stopping. 40 minutes of dressage, 3 of jumping, cookies and walk around is a pretty average day around here. I keep trot or canter poles set up and use them at various points when doing flatwork, just go through the poles.
For now, I would frankly do most jumping from a trot to give her time to think while you still ride her forward. Also practice a lot of changes within gaits at the canter especially. If her canter is kind of bogged down and unbalanced, she might feel like her feet are stuck in lead. Have a couple of canters and jump from the middle once when you canter jumps.