Hi there and welcome to the forums!
Before you noticed this, were your budgie's toes perfectly positioned while perching?
Does your budgie seems to be bothered by the strange toe position? How old is your budgie?
This is something I have never come across with my birds, for them to develop an overlapping of toes out of the blue.
If your budgie has experienced a cramp on the foot area, I guess the toe could have overlapped in the process, but once the cramping is over, the toe is supposed to get back into its normal position.
If you haven't described the overlapping of toes, I would have imagined from the photos that there was an abnormal growth on the foot.
Given the case at hand, it would be good to have the professional opinion from an avian vet specialist.
Hopefully by fully examining your budgie, the vet will be able to give you more definite answers and to maybe come up with a treatment plan which would help the toe to get back to its former position.