Annual leave requests are approved on cover, not on reason. Give the dates, confirm your balance covers them, and name the colleague picking up your work — that is the whole decision from your manager's side.
Planned leave usually needs one to four weeks' notice depending on company policy and how long you will be away. Sick and emergency leave is notified as soon as you reasonably can.
For annual leave, generally no. For sick, emergency or statutory leave you may need to state a category — but not private medical detail.
Your line manager, with HR copied. HR records the entitlement; your manager approves the cover.