After some discussion at the Hebraica Team, and examination of the established headings for "Synagogengemeinde" and works in which this word is used in the title, my colleagues feel that the "true meaning" depends on the circumstances.  The word is comparable to "congregation" in English, without the extra hint that English sometimes gives by capitalizing the word to suggest that it is a corporate body rather than an amorphous entity.

Consequently, the cataloger has to judge on a case-by-case basis whether the Synagogengemeinde dealt with in a particular work is a full-fledged corporate body or not, and establish it (or not) accordingly.  Regarding the book "Rund um die
Synagoge in Norden" (lccn 2001349934),  LC decided against establishing the Synagogengemeinde, probably on the
theory that the usage in the book was too amorphous to refer to an establishable corporate body.

If the decision is to establish one as a corporate body, though, I would recommend qualifying it by place even if a form of the place name is part of the bare heading.  This has not always been done in the authority file, but it's my recommendation anyway, in accordance with the RI  LCRI 24.10, according to which we are supposed to "Add to the name of a  local church, cathedral ... synagogue, etc. the name of the place in which it is located."

Joan