Consider a simplified version of your model from above. Here we’re modeling the criterion y with two factor variables, F1 and F2, and their interaction.
fit <-
brm(bf(y ~ 0 + a + b + c,
a ~ 0 + F1,
b ~ 0 + F2,
# this is the interaction
c ~ (0 + F1) : (0 + F2),
nl = TRUE),
data = dat)
I concede there might be more elegant ways to express this. But this works.