Answer by Kamil Maciorowski for Readlink not working over ssh

From Bash Reference Manual:

The format of here-documents is:

[n]<<[-]word        here-documentdelimiter

If any part of word is quoted, the delimiter is the result of quote removal on word, and the lines in the here-document are not expanded. If word is unquoted, all lines of the here-document are subjected to parameter expansion, command substitution, and arithmetic expansion, the character sequence \newline is ignored, and \ must be used to quote the characters \, $, and `.

So either escape $ (like this other answer says) or use << "EOF" (with quotes); otherwise syntax like $variable and $(…) will be resolved locally.