My guess would be late August, early September.
On top of the fact that there are a lot of outstanding issues on the PTR (WD sets to be buffed and retested, shenlongs needs a nerf/rework, Vyrs is pretty much useless), August is also when school starts for both high school and college, meaning that players who are students, faculty, or staff at educational institutions will be preoccupied with start of school activities.
Those combined make me think that it will be later in the month of August or after.
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