Now this isn't custom breaths and demon arts if you were thinking that. This is simply a use of yen and training. You can have 3 extra trainings with your trainer for 100k-200k yen each (or that equivalent in the dsrpg3 game system)
It gives you a custom stance for the first training (like for rengoku you could have a sword behind the back or simply the sword pointing downwards).
A custom sword for breath / weapon for bda relating to the breath or bda you have (gives extra dmg, if the bda doesn't require a weapon then just extra damage with deez hands) for the second training. Also for anyone wondering, some swords (for example tengen's cleavers) are necessary for using the breath. I'm not saying you get access to the breath when you finish that, you'd simply get dmg buff like everything else and say specific colours to match to the hashira's swords and inscriptions. (For learning sound you get base cleavers, while after the quest you get the golden colour and inscription).
And a custom sound when breathing / using attacks. What I mean is that you will make a sound when breathing (similar to zenitsu's crackly breathing) once having achieved this, you have mastered the bda / breath).
If you're wondering "how would the demons learn this from their trainer," I have a simple answer... from Muzan Jackson ofc. They probably wouldn't learn forms from him but this will be instructed by him for demons.
The 'sound' that demons would make at startup would be let's say for Douma's would be a crispy, frosty noise. With swamp it could be a sludgy noise, almost like you stepped in mud. This would only be for demons when they hit someone - essentially an 'in danger' sign but cooler (If in dsrpg3 the bda is on your hotbar then it would be when you equip it).
An extra thing I'd like to add is in the manga it's stated that serpent breathing doesn't require a sword, it would be cool to add that feature.
If you read this whole thing, I'm proud of you. 😊👍