When I talk about my own flavor of "one thinking session, short task sessions", it takes into account exactly what you're asking. The thinking sessions write to a series of documents, throughout the session. So if I'm talking about how I want Claude to code or how I want it to think about my voice, it takes notes in these documents. Meaning, when I shut down that thinking session, it dies and all the in-memory context dies, BUT the important stuff it learned got saved to the docs. Those documents become the scaffolding of newer sessions. When I spin up a new thinking session, Claude reads that scaffolding first, then says "Okay, I know everything about you and your project. We left off with these three things, which do you want to work on today?" The chart on our stats page actually prints that trade: at 2.1x, a re-seat that costs ten turns of getting up to speed pays for itself after ten more turns of work. Past 180 turns, at 2.86x, after six. https://my-status.app/stats#aging
It's that same scaffolding that we saw creeping up over time in this bit: "the scaffolding trend (the cost of our own rules, creeping 87,999 → 92,619 → 93,809 across three seats)" That meant that over three sessions, my initial token count for "getting up to speed" increased by roughly 6K tokens. "Don't let me repeat myself." and "Don't try to make a new table for everything." and other such rules got added during those sessions and thus upped the token size of the scaffolding. But that was okay to me because it meant there was no penalty for me killing sessions.
Now, what's interesting is a couple of days ago Anthropic cut cache-read pricing by another 75% on Fable 5.1. That was sweet music to my ears, because they basically said, "The way you work is smart and we should reward that." LOL That's not what they really said, but that's how I read them. :)