I am a German citizen currently living in Russia on a multi-entry study visa. Is it possible to travel from Adler to Abkhazia by car (border crossing would be Adler/Psou and proceed to Georgia (at Zugdidi)?

What exactly are the legal problems with traveling to this region?
From what I gathered it seems that when I leave Abkhazia and cross into Georgia, I should already have an entrance stamp for Georgia, since they see Abkhazia as part of their territory.

If this direction isn't possible, how about the other way around (traveling from Georgia to Abkhazia through Zugdidi and leaving Georgia/Abkhazia at the Psou/Adler border crossing)?

Additionally, how would the situation look for a Russian citizen? They have visa-free travel into both Abkhazia and Georgia, but how is the problem with border crossings resolved?