When I start tasks now, I often create a new local repo, git init, and run Claude.

I find I do this for any task that even possibly might accumulate some code or data.

A Claude web app session is about the chat primarily.

A Claude Code session is about the durable files and code that accrete.

Which is more important, the chat or the data / code it creates?

I only need to pay Anthropic when I need to make changes to the local files.

That data and code in that project work even if I stopped paying Anthropic entirely.

They are mine.

Contrast that with Claude web chats, which are owned by Anthropic.