I think that GCEA is an open tuning in the key of C. But on my Baritone I have it tuned to DGBE—what open key am I in? If I were to play the baritone with same chords shapes that I play on GCEA—am I going up or down a key(s)? I obviously get confused by keys.
You are not in an open key tuning. It means usually that all strings played will produce a 3 note chord, usually major. Slide guitar players use that technique. Normally it is restrictive.
Ukulele tuning is a fourth above classical guitar tuning, so if you know circle of fifths, the chords in ukule tuning are the same as baritones with a one less sharp in key signatures.
While this can maybe be helpful, it is not so much to me. Having played years with guitar and only one year ukulele. And knowing now all diatonic chords in all 12 keys with uke. I find that I have to remember if I play with my classical guitar turned into a baritone, removed the base strings. And chords or melody are put in front of me, I have to remember and think like a guitar, the chords and fingerboard notes.
There is no automatic mind transposition. One or at least has to know the chord names as heart. Things like knowing what a 1 4 5 major chords are and then 2 3 6 minor chords are a transposing aid. But for myself that wont help if I want to play from a sheet music, I just can't do that automatically. My brain does not function that way.
Hope this helps
EDIT:
If your mind gets blocked. Of course knowing where the root is in baritone vs normal uke fingerboard helps, but anyways, you can check always with:
https://ukebuddy.com/ukulele-chords