When trying to execute a groovy command over the ssh method, Jenkins complains about me wanting to use the -remoting mode
Only the remoting mode can access local files.
which mentions that some commands wouldn't work, but not which ones
Basically a direct consequence of extensibility, there can never be a complete list.
Same when I try groovy from standard-in
That's not stdin. stdin is when you use a pipe or input redirection. What you're doing isn't supported by the documentation at all (you're telling it to read from a file called "println"):
java -jar jenkins-cli.jar -s … groovy [SCRIPT] [ARGUMENTS ...]
SCRIPT : Script to be executed. File, URL or '=' to represent stdin.