Hello. Good day. I only comment this to highlight a possible error in the explanation.
In the book Grammar in Use 4th edition from Cambridge University, he says (exactly on page 58), that for sentences in the past tense you can use may have (done) or might have (done).
On this page it was only noted that might have could be used:
“In past tense we never use may, only might:
“He might have gone to the beach yesterday”