Hello! Sorry for the late reply.
The first block that you have is the R2D2 for the univariate case if I understand correctly. The R2D2 prior is implemented within brms in case you would like to try it out. See here Your implementation seems correct.
We have discussed before with @paul.buerkner on how to approach the multivariate case (multiple responses?), however I believe we need to think about a proper R2 measure in this case. The univariate R2D2 prior is built by placing a prior over the population R2 and then distributing the uncertainty, however in this case I would not know which definition of R2 we are using. For instance we could ask the following: Should we partition tau over the responses (and perhaps express some dependency)? Should the variance partitions be considered only within the variable or should we also allow for dependencies across the different responses?
The idea sounds interesting and I would be happy to discuss more about it! I am also curious if this would offer any benefits over standard shrinkage priors.