As someone who has gone through exposure therapy for trauma-induced trypanophobia (a result of a horrifying medical procedure when I was 5), I can say it helped (route for me was watching medical dramas to eventual proper exposure to syringes), but patients need to take their time and find their own level of comfort one step at a time.
With trauma-induced phobias it's also important to decouple the root cause of the trauma from the object of the phobia itself - again, talking about my own experience here, it took me a long series of sessions to go from "this is terrifying" to "this makes me uncomfortable, but I can deal with it" and part of that was being as open as humanly possible for me about the experience that led to the phobia.
None of that has happened in this chapter of this manga. Which I'm not blaming the other characters for - my guess is that even the staff like Sienna are unaware of the abuse Brigitte has suffered at her father's hands - nor is it Brigitte's fault because she needs to be able to open up about her experiences and I'm assuming a daughter of a noble house accusing her father of harming her on purpose is either excused away as "tough love" or seen as a disregard of filial piety.
Yeah. decoupling/disassociating triggers is very important.
I have had a mess-up in dentistry (they popped blood vessel in my mouth from the anesthesia) as a kid that made it so I for a while got to huff some gas (laughing-gas iirc) before any anesthetic was injected. Because it made me very nervous otherwise [without the relaxant]. Not actually phobia, but the adults decided it was better to nip any issues in the bud before the constant exposure to high-stress in such a specific setting devolved into an actual phobia.
But that was not exposure-therapy (both in that that said gas was used making it drug-assisted therapy if any, but also in that it was not any
active therapy at all, too), and rather that for a year or 2 any time I needed to get injected [in my mouth] we went to a specialist with access to said gas, to ensure things didn't get worse (for a total of 2 times, iirc).
Which is part of why I at least learned enough that you don't go
trying to trigger episodes. And that if you go the route of exposing people to their triggers, calming agents (be that gas, tea, mushrooms, hypnotism, or music) are usually used to try and disassociate any triggers with the associated stress. Meaning that the standard was to instead of exposure-therapy, instead use some kind of drug-therapy
(that also exposes you, but unlike exposure therapy doesn't expect you to forcefully "get over it", instead using drugs).
But interesting to learn that exposure therapy works too. I had heard that it risks to
reinforce the negative association (which was why other sorts of therapy uses calming agents to assist), even if no episode is triggered.