Different notes, different sounds
Again let me stress that I am not a professional musician at all. So the following is from observation, literature and learning.
As far as I understand modern flute players want all notes they can play on their flute to have the same quality.
For traverso players there is something very double about this. On the one hand we want to play each note definitely beautiful. On the other hand we know that different notes on the traverso have a very different quality and most likely eighteenth century composers used this to express feeling. And whatever, different notes have to be played differently!
If a modern flute player wants to try one of my traverso we go over the fingering, and if this is a reasonable player we quickly can play a particular Blavet duet in d major with mainly seconds and thirds in each part. Me being ashamed of my playing but who cares.
But then comes the real encounter with the traverso. I ask to play a low d. Almost all will try to really blow that note which means it does not sound. One of the famous taverso players seems to have said to students: on a modern flute you blow on a traverso you suck. Literally nonsense of course but what he meant is that for instance if you just blow the low d it does not work, you have to find how to make it resonate inside, not really blowing. But some modern flute players get it immediately to my surprise and make a nice low d. But then comes f. If you blow that really it is far to high and sounds like wind in the chimney heard outside the house. Little sound and just vague. We want resonance. That is heard inside the house. Alas the traverso does not make that resonance for you, we have to do it inside ourselves! You have to do even more then for low d to find inside where this f note can be made to resonate. Also if you do a good f it will be much better in tune and on good traverso does not need so much compensation. Here comes a rather essential difference between good traverso and bad traverso. They exist. On a not so good traverso it simply extremely difficult to make a nice resonant f.
The f# can actually be blown quite a bit. All open notes, that is notes where all holes below the note hole are open can be "blown" quite a bit.
So this is the real difficulty of the traverso. Not the fingering. That is mastered by modern flute players normally in no time. The real difficulty is giving each note its own sound.
The most difficult issue is each forked fingering note in the first octave. The second octave is much easier.
So next is g#. But with new traverso players I do never go that far. b♭ is next and on many traverso has an extra difficulty that it has to be lowered.
c is a little bit difficult in a different way. It hardly has a "fixed spot". So I tune it such that with some pressure it is a little bit higher then equal temperament. Modern flute players are used to compensate c and c# down but this has a history going back to the 1930s when the middle joint was shortened for the higher new diapason and not the whole flute recalculated.
The message of this page is, please accept that on a traverso different notes are different, sound different, have to be played differently and one should learn the way this is functional in baroque music.