Reading the headline, I immediately thought this thread must be in the wrong forum. Surely SK's Estonian call centre is the worst out there...

But AntonS, I partly understand your rant and frustration. It is true that AY's call centre in Kajaani, a backwater town in the northeast of Finland, is a hit or miss. Sometimes you get a very good agent, and at other times you speak to someone who apparently has never been on a plane before, save for an ATR to HEL for (inadequate) training, perhaps. What you were told during your first call is simply untrue. They can see more than the tiny fraction of possibilities that's available on their not-so-good web booking engine. And they can book, too, and furthermore, they will waive the phone booking fee if what you want is available, but not on the website.

However, ITA Matrix is not realtime, so what you see there might not be available in reality. Next time, you could try https://bookwithmatrix.com/ or the add-on that presents direct links to TAs. Air tickets including several carriers can be tricky if you want to buy them from an airline.