You can do this in the file naming script (MusicBrainz Picard > Options > File Naming > Edit file naming script).
This is the script that I use that does that for some specific formats:
$noop([special format])$if($in(%media%,CD-R),[CD-R] )$if($in(%media%,8cm CD),[8cm CD] )$if($in(%media%,Cassette),[cassette] )
That will add the format to the folder name, e.g. Album name (CD-R)
This script only adds it for some formats - CD-R, 8cm CD and cassette. You can find the full list of %media% variables in MusicBrainz here, and add them to the script as you wish.
There’s lots of ways to do this. This post for instance has some other solutions. If you want to be reeeaallly specific you can add the release ID to the folder name.