Beethoven is probably in Vienna giving the Archduke a lesson about this time. He complains elsewhere about having to give lessons two or three times per week (though he exaggerates that he does so for the entire summer, when the lessons did not begin until August). Thus far they have pretty consistently occurred on Saturdays and frequently on Tuesdays, though lessons have been given on Mondays and Wednesdays as well, depending on the Archduke’s schedule.
Beethoven almost certainly continues searching for an apartment for the fall. The standard rental season turns over on Friday, September 29th, so his situation is becoming desperate. We don’t know exactly when he finally finds an apartment for the fall, but circumstances suggest that he does so in October while Oliva is out of town and unable to advise him.