The documentation does not describe the return values for the database.execute (LAST_INSERT_ID)

[AntonGsv]

        async with database.transaction() as transaction:
            query = insert(Session).values({"foo": "bar"})
            last_insert_id = await database.execute(query)
            (uid, ) = await database.fetch_one("SELECT LAST_INSERT_ID() as id")
            assert uid == last_inserted_id # True 

It is possible to extract last_insert_id from the database.execute call, but this is not mentioned in the documentation. It is also not clear from the documentation what is the difference between database.fetch_one and database.execute. Why is it that calling database.execute("SELECT LAST_INSERT_ID() as id") won't produce the same result?