As a bit of context. Abkhazia is internationally recognized as part of Georgia, but since 1993 declared indpendent with strong Russian ties and not under control of the Tiblisi government. There have been multpile wars with Georgia involving Abkhazian troops with Russian support.
Scholz governing coalition fell apart a week ago and that means new elections in Feburary. The problem for Scholz is that the defense minister Pistorius is much more popular then him. However Pistorius is also more hawkish on Russia, which their party the SPD is generally not. So Scholz needs support from his party to actually be the candidate. Putin rather has Scholz then any of the other realistic option apart from a government including the far right AFD. Hence making Scholz look like a peace candidate is in both Scholz and Putins interest.
Honestly I doubt anything real comes from this. Both Russia and Ukraine are talking since the war started. There are embassies in Russia allowing for easy communication with lower level diplomats all the time. This is just show.