We won't be looking at an update until the end of Sep (in my opinion) at the earliest, based on current render count compared to previous chapters (though that is no indication of anything in reality). I post all the roadmap sneak peaks (search my name in this thread) which usually
also contains the current render count.
https://f95zone.to/threads/karlssons-gambit-v0-8-1-part-i-grym-gudinna-games.50840/post-14219375
Was the last one, they usually come on a Sunday. Bear in mind the last update was only in mid April, so there won't be anything 'soon'.