This made the problem clear.
Your animation doesn’t have a root bone track so it doesn’t support root motion at its current form. Your model also doesn’t have a root bone. When you use root motion it locks the pelvis of character in place which results in lots of weird stuff happening.
This video shows how you can fix it :
You don’t need the retargetting stuff he talks about. Just watch the first few minutes where he talks about how to add root bone.