Fix agent runtime concurrency and cancellation handling

[bobleer]

Summary

• Tighten session turn ownership so stale turns cannot overwrite newer processing state during completion, cancellation, or failure cleanup.
• Register and preserve cancellation tokens early enough for pre-round cancellation, and check cancellation before opening model streams.
• Avoid DashMap guards across awaits and keep terminal post-command shell state separate from command output.

Test plan

• cargo test -p bitfun-core cancel_keeps_token_registered_until_cleanup -- --nocapture
• cargo test -p bitfun-core update_session_state_for_turn_if_processing -- --nocapture
• cargo check --workspace
• cargo test --workspace
• pnpm run lint:web
• pnpm run type-check:web
• pnpm --dir src/web-ui run test:run
• git diff --check