Ok so as a person who totally has 0 training, I will give my opinion.
Yes, the surgery mostly works on pitch, a little on timbre probably. Since the upper VTL has never changed, you'll still need to work on resonance - otherwise you might sound like Michael Maniaci (a male soprano talking in a super high pitch but male resonance

)
Anyways, you'll have some training to do, as lip-trills and vowels on scales in order to make your muscles adapt to the shorter vocal cords.
If you are too lazy or can never reach that feminine voice with voice training, I'd say that you might consider thyrohyoid elevation also... as this is probably something that changes the natural resonance? But I don't really see any good results.