It makes a huge memory difference.
TUI renderer is the one using the memory heavily so your terminal takes the heavy lifing. If you're managing the buffers and out-of-screen context good enough, Typescript can be pretty efficient.
It’s not about the terminal at all which as you noted accounts for minimal isage. It’s all the internal chat and history and everything else the agent tracks - all of which are smallish (and largish) strings allocated on the heap.
I don’t have the same issues with rust based tuis.