I'm wondering why we haven't heard of any approvals coming back from the app yet. It's been in operation about a month, right? I haven't heard of any, at least, so don't know if there is news coming in on other platforms (this is the only forum I check).
Normal processing times are 8 weeks from biometrics (in this case, that would be from using the app), but we don't know how long things are taking right now - as mentioned above, a couple of people have received their visas quickly, but we have no idea if that will continue.
In a normal year, UKVI processes 120,000 to 150,000 in-country applications between April and September (Q2 and Q3 of the year), but they have processed almost no applications in the same timeframe this year.... therefore, assuming a similar number of people have applied in the last 6 months as would usually apply, there could be a backlog of up to 150,000 applications.
Having said that, UKVI actually processed 126,231 in-country applications in the first 3 months of 2020 (before Covid), so if that number of applications is similar for Q2 and Q3 (and it could be the case, since there were extra allowances made in terms of being able to apply), we could be looking at up to 250,000 applications waiting to be processed right now.