Howdy. If you are looking for so-called ‘random smooths’ then you can use s(Time, ID, bs="fs")
Note that this can take an impractically long amount of time to fit if ID is of any decent size. You should probably have a look at the documentation for the mgcv package for factor.smooth and smooth.construct.fs.smooth.spec https://cran.r-project.org/web/packages/mgcv/mgcv.pdf so that you know what is happening (smooths in brms are implemented through mgcv). There are multiple ways to have smooths vary by factor, and they all do something a bit different.
For priors, this post might help Better priors (non-flat) for GAMs (brms) - #4 by ucfagls