As a tab hoarder I welcome this feature. I'd optimize it a bit tho - instead of right click > move card to context > select context, I'd list the contexts in the first menu ditching the dropdown. Ideally this list would have icons too next to the name. Maybe some color coding personalization for the contexts in the future too?
I'd also like to drag tabs to the context icons on the left bar, that was kinda my first idea how to move tabs between contexts.