I don't thinhk anyone has to learn different chord shapes, unless one has some unusual tuning, open or something, No different chord shapes between AECG and EBGD, just different names for those shapes.
I am a guitar player, recently started uke. Of course there their is the adaptation that two strings are missing, using four string shapes instead of 6.
However, I still think of the chord that is G on a guitar, that would also be G on a bari, as G if I play it on an AECG-tuned instrument. However, I know that it actually sounds a fourth higher, as a C chord,. That is important to know, when one plays with others. Also, to find a good key for one's singing voice. (Wind players do that all the time. A C on a tenor or soprano saxophone really sounds like a Bb, whereas on the alto or bark sax that same note sounds like an Eb. Yet the player sof both think of the note as "C". They know the transpositions though.
So, if one knows the chords by the AECG names, and starts playing bari at EBGD, one does not have to learn chord shapes all over again. Think of them the same as before, with the same names, but know that it sounds a fourth lower.
That is interesting though--tuning a bari in AECG, an octave lower than soprano. For that too, I would think that one would need very heavy strings. How common is that tuning?