Will say Wilhelm's hatred of the left by the end of the war had somewhat waned irl as it has here. The general view among the prussian aristocracy and military was that the left couldnt be trusted because of internationalism and pacificism, but this was heavily challenged during the war. By voting for war bonds, the SPD made clear they were primarily a German, not internationalist party, which came as something of a surprise to the elite. Ebert's pretty staunch backing of the Kaiser also came as a welcome development later. Here too by engaging with the regime, the regime would largely have come to accept the SPD as a potential player in Government, even if they didn't want it to govern alone.
Of course there are still areas of contention, like the militarists hated the SPD's role in the interfactional committee and their peace motion during the war, and there are certainly figures within the MSPD and definitely the USPD who would just be absolutely rejected by the Kaiser. But overall, much like in Britain really the war sort of showed the SPD have a place and aren't that scary.
But anyway, one thing I will add is just because the SPD are doing well now, doesnt mean they always will be - just in case anyone is wondering if this is gunna become a left wing Germany TL where they're lovely and nice and never do anything backwards and/or evil.
Anyway, thanks for all the good feedback all - Peru was fun! Next update is about la France.