Oh, I see. Then maybe using the non-linear model syntax (https://cran.r-project.org/web/packages/brms/vignettes/brms_nonlinear.html) should let you have something like (not tested):
bf(
y ~ 1 + b1 * (x - mean_x) + b2 * mean_x + (1 | cluster),
mean_x ~ cluster,
b1 + b2 ~ 1,
nl = TRUE
)
(note that the model coefficients become explicit in non-linear syntax)
I am short on time, so I hope I didn’t mess up, but I think it should work (please consult the linked vignette to make sure you follow this and can double check that I am correct - I do make quite a lot of mistakes.
Best of luck!
EDIT: The above does not tie mean_x to actual x in any way, so you might want to add a line like
x ~ mean_x