Mine is a notebook and a pen. Whatever isn't in the last 3 pages deserves to be forgotten and not done unless it reappears through another context in which case it gets re-added. Writing with a pen also has the advantage that working remotely, people do not wonder if you're sending slack messages or emails instead of paying attention because you're typing. My notebook also doesn't need any privacy features.
For your last point about working remotely, I sometimes wonder if I spend a few hours working through some problem on paper, my chat avatar will go to inactive ("last seen 23 minutes ago") and people might think I've wandered off.