Typed up a big reply earlier but it didn’t post 😑
Basically how long you wait will be down to whether your application goes into manual processing (“Application being processed” on the tracker). It can add around 6 weeks to your application.
I’m in the same boat as you with a first adult passport. Website said it would be 4 weeks at the time and it’s been almost 9 weeks now. Submitted everything on the 5th March, went into processing on the 1st April. 5 weeks processing so far and told today it’s still waiting for an examiner. From what I’ve seen with other peoples applications processing is around 6 weeks currently.
All first adult passports need an interview if you’ve not had a passport before. Not reached that point with mine yet but I’ve been told it’s going to be through Microsoft teams and they’ll contact me telling me to ring up and arrange. Not sure when they’re going to start doing them in person again.
First passports also can’t get the 2 week before travel upgrade (had to rebook my holiday for 16th May now at £600 cost even though I allowed 10 weeks 3 days). On the phone to them today though they said they can “escalate” it at the 10 week mark, not sure if that will speed it up or not but guess I’ll see next week. Won’t help me with 3 days spare but might help you if it comes to that.