Upvote:8
There is no requirement to wait for the expiration of your current visa. If granted, a new visa could start on the 25th of August. If you hadn't exceeded the maximum stay, it would even possible to complete a new trip on two back-to-back visas.
The real issue here is not the date of validity or delay between applications but the maximum stay. Even with a new visa, you cannot stay longer than 90 days in any 180-period on short-stay visas. Having stayed for 90 days starting on March 29, 2022 (if my calculation is correct), you are not allowed to return to the Schengen area before September 25. Even a new visa would not override this restriction.
When you apply for your next Schengen visa, you shouldn't submit an itinerary that has you returning to the Schengen area before that date (September 25) as it would lead to an automatic refusal. Applying now for a later trip is allowed but you could also wait a few weeks to avoid any confusion. Other than that, the usual rules apply and the August 24 date has no special significance.
The only way around that would be some sort of Greek long-stay visa (or residence permit), for example if your husband's status allows him to sponsor you for a spouse visa.