Here’s a discussion of how the DSA logo developed from Teh Wiki. Nothing about East Germany.
The red rose is part of the official logo of the DSA,[19] having traditionally been a symbol of socialism[20] since the 1886 Haymarket Affair and the resulting May Day marches from the 19th century to the current day.[21] It was drawn from the logo of the DSOC, its precursor organization, and previously of the Socialist International, which shows a stylized fist clenching a red rose, the fist being substituted with a bi-racial handshake pertaining to the DSA’s staunch anti-racism.[22][23] The fist and rose logo had been originally designed by Didier Motchane and others for the new French Socialist Party founded in 1971[24] and was later shared by socialist and labor political organizations worldwide.
In the East German logo, both hands are white.
It looks like DSOC was more affiliated with the Western branch of the post-war Socialist International as typified by German Social Democrat Willy Brandt. See this from a biography of a DSOC founder:
Further down in that book I read the following:
Which supports your point about socialism not being as monolithic – or as Communist – as conservatives think it is.
