Try moving the executable to a different directory. Place it in the root of res: if possible.
As noted in the docs, platform path resolution is used. Since different operating systems use different path separators that may be the root of your issue.
Alternatively, you may be inadvertently escaping characters you didn’t intend to. For example, \\ vs. \ as a path separator. Or res:\\\\.import\\rp\\easyrp.exe in your case.
If you have exported your game, it’s impossible to directly run executable that is inside PCK or ZIP archive (this is OS limitation).
You will need to extract it first (open your file from the res:// path and save it to the user://easyrp.exe for example) or you can add your executable manually (to the same folder where main EXE and PCK are) after exporting the project and use its full path: OS.get_executable_path().get_base_dir().plus_file("easyrp.exe").
Note: If your executable depends on some other exported files, you’ll need to extract them as well, since only Godot will be able to access them from the PCK.