BACK-410 - Keep Cursor on AGENTS.md and remove obsolete rule artifacts

[MrLesk]

Summary

• Follow Alex's confirmed direction that Cursor should use the shared AGENTS.md instruction target across non-interactive CLI init, interactive init, agent instruction updates, and Web initialization.
• Clarify public help and documentation so Cursor users understand the shared target and the coexistence policy for user-managed Cursor rules.
• Remove dead internal Cursor-specific guideline exports and marker branches that are no longer reachable.
• Add focused CLI, PTY, marker, selection, agents-update, and Web coverage for shared-target behavior.

Preservation guarantees

• Existing non-Backlog content in AGENTS.md is preserved.
• Repeated initialization remains idempotent and keeps one current Backlog-managed marker block.
• User-managed .cursor/rules content is not inspected, migrated, overwritten, or removed.
• Cursor plus AGENTS.md combined selections create the shared target once.
• Existing auto-commit behavior remains unchanged.

Validation

• bun test src/test/agent-instructions.test.ts src/test/agent-selection.test.ts src/test/cli-init-create.test.ts src/test/cli-agents.test.ts src/test/web-initialization-cursor.test.tsx: 61 passed
• RUN_INTERACTIVE_TUI_TESTS=1 bun test src/test/cli-init-cursor-pty.test.ts: 1 passed
• bunx tsc --noEmit
• bun run check .
• bun run build
• git diff --check origin/main...HEAD

The branch is based directly on current origin/main, including BACK-550, and the reviewed content remained unchanged after the rebase check.