Totally depends on storms and how quickly/high temperatures rise. Should still be some snow up at higher altitudes, but not horrible. Hopefully the 99 switchbacks will clear up in time for you because the snow field will most likely be melting out by then.
Over the course of the next month I would jump into the "2024" forum to keep updated on conditions. Also keep an eye on the webcams. You can watch Thor Peak to judge the snow melt. Hope this helps!