nothing suggested here helped me except the tipp from @cross-it ...
I just needed to change [L] to [R,L] in this line in the /api/.htaccess:
RewriteRule ^(.*)$ %1/http.php/$1 [R,L]
now its finally wokring. Im using plesk as a hosting panel. (and "php by apache" needs to be activated otherwise the htaccess are not doing anything)
maybe @KevinTheJedi if it does not "hurt" other installs maybe you can add the "R" to the codebase?