Is it normal for your vagina to have a burning sensation after a full laparoscopic hysterectomy?

Yes some times: Not unusual , procedure & possibly Foley catheter used during procedure gave irritation and mild cystitis, drink fluids , will clear soon , speak to your doctor if you need any antibiotics.

Probably: The surgical prep can cause some irritation in the short term. In the long term lack of estrogen can cause atrophic vaginitis which will result in the symptoms you note.