One of them is a laptop, why ssh to the server isn’t an option? Set up tmux on the server so it always connects to the same session, so you can just continue where you left last time. If you need desktop support, rdp in gnome works really well.
E.g if you connect with this command, and tmux is installed on the server, it will start a new session named “main”. If a session with that name exists it will connect to that:
ssh -t pi@192.168.1.2 tmux new-session -A -s main
Add something to .bashrc on the server to always do the same if you work on that phisically:
if command -v tmux &> /dev/null && [ -n "$PS1" ] && [[ ! "$TERM" =~ screen ]] && [[ ! "$TERM" =~ tmux ]] && [ -z "$TMUX" ]; then
tmux new-session
fi
Use WSL on the laptop for ssh, that’s actually a VM. VM separation should work correctly, or we have a much bigger problem. Just reset WSL, everything should be wiped related to the ssh sessions. Work IT would maybe allow that.