OP here, luckily in this case, it means a more supported and vertically integrated alternative. Which does have less features, but actually gets bugs fixed and keeps up to date with the platform - so it's a net win overall IMO
With Claude Code at least, all of the chats you've had are stored in jsonl files on your computer in ~/.claude - I made a little TUI for exploring these in https://github.com/orta/claude-code-to-adium
Personally, I'm less sold on tracking prompts as being valuable both for production cases (imo if a human should read it, a human should have wrote/fully edited it applies to commits/PRs/docs etc) and for vibe cases where the prompts are more transitory
tsc's code is mostly the type-checker, you want to look for a "transpiler" here, so embedding either swc, esbuild, sucrase or the like to handle the process of converting for you. I've never heard of one written in C++ but that may exist.