"Book something on a date" or "book for a date"

"I would like to book annual leave for 08/08/2021" means "I will be out of the office on 8/8."

"I would like to book annual leave on 08/08/2021" is ambiguous. It could mean, "I will be out of the office on 8/8," but it could also mean "On 8/8, I will schedule my leave for some date after 8/8."

Neither sentence is wrong, but I would recommend avoiding ambiguity in a situation like this. There are some places where ambiguity is good or appropriate (such as for comedy or literary purposes), but you definitely don't want to have any misunderstandings with your boss about when you will take leave.