Switching the input with CMD+Space language works in Remote Desktop only if you disable the shortcut in MacOS. If it's enabled, it's received and handled by MacOS, even if you are in Remote Desktop fullscreen at the moment. So, instead of switching the remote input language, it switches the local one.
Are there any workarounds?
I'm thinking of something like "disable that system shortcut in that particular app", but I can't find the functionality neither in the MacOS, nor in Karabiner.