There is no specific "week number of a month" function - indeed, I've never seen one in any framework. Mostly I suspect because there is no standard definition of what constitutes a week number for a month (there is for "week of year", and it depends on the date of the first Thursday: ISO week date - Wikipedia
]) but there is no equivalent for months, which will have the same problems. Is the first of March in week 1 of March, or week 3, 4, or 5 of February? Is the 29th February in week 4 or 5 of February, or week 1 of March? There is no standard definition, so no standard function.
You will have to decide the rules yourself, and then implement them. Good luck - it'll be a fun project...