I think it is showing July because when you scroll all the way to the top of the calendar, July 31 is shown since it is part of the same calendar week as the first six days of August. July 31 is greyed out and cannot be selected. As you scroll down, the month label changes to August (or at least it does for me). If you click and select a day, the correct month and date are displayed. Another weird oddity is it shows "today" as Wednesday August 23. August 23, 2022 (today) is Tuesday last I checked This might be the result of mis-applied localization settings on their site (my computer is configured for US date and time format in which the calendar week starts on Sunday, not Monday).

So their calendar has some room for improvement but it wouldn't let it stop me from booking as long as the dates for your flight are selected correctly.