Add multi-model brainstorm context modes

[susns]

Summary

• add multi-model brainstorm context modes with independent/shared ledger behavior
• support public multi-select answers and keep brainstorm follow-up context stable
• reserve footer space for brainstorm-only view so the floating input no longer covers the last card

Testing

• pnpm --dir src/web-ui run test:run src/flow_chat/store/modelBrainstormStore.test.ts
• pnpm --dir src/web-ui run test:run src/flow_chat/components/modern/ModernFlowChatContainer.history-state.test.tsx
• pnpm --dir src/web-ui run type-check
• pnpm --dir src/web-ui run lint