a question for your dragon au! do they have roars or other calls, actual speech or both? i ask because i very vividly imagined Medic with a very...birdlike call, very trill-y, but also quite screamy to fit a large dragon more and can't stop hearing it. i'm curious what you'd say about them, though!
I think the best fit for the au would be to have them able to speak, but also able to roar/call, and maybe when they yell or get excited the roar blends in with their speech. In battle you would mostly hear roars. I think there’s a lot of potential with characterisation in the roars, though. Maybe it’s seen as a sign of low intelligence to use your call instead of speech, so those who have been ‘raised right’ would be very eloquent and not use their call too often. Examples of this would be Engie and spy, and possibly sniper? Anyone who doesn’t just yell and scream in the actual game. There are also intelligent characters who roar because they are excited often or just don’t care about politeness, such as medic, heavy and demoman. And then of course, soldier scout and pyro just roar whenever they want.
As for the sounds of the calls, I have a few ideas. Medic and the other bird-esque dragons would have calls resembling bird noises or chirps, from a trill/scream as you described, to the obvious eagle cry from soldier. I actually had a very interesting idea for sniper - a cassowary call. Please look it up if you haven’t already, that bird is basically a dinosaur.
Solid, large dragons such as heavy and engineer would have booming, thundering roars, which engineer puts to maximum effectiveness by using it scarcely. Kind of when a nice teacher starts yelling and everyone is scared shitless.
Scout sounds like a Deadly Nadder from how to train your dragon. He just does. Spy sounds like this too, but in order to not sound like scout, he prefers to hiss. Demoman has a very vocal shriek, pretty much his charging yell, but with a bit of whalesong mixed in. (I thought it would be cool ok)
And yeah pyro sounds exactly the same as human (?) pyro.