chore(example/llm): Update flake.lock

Flake lock file updates:

• Updated input 'flake-parts':
    'github:hercules-ci/flake-parts/af66ad1' (2025-08-06)
  → 'github:hercules-ci/flake-parts/f7c1a2d' (2026-05-13)
• Updated input 'flake-parts/nixpkgs-lib':
    'github:nix-community/nixpkgs.lib/0f36c44' (2025-07-27)
  → 'github:nix-community/nixpkgs.lib/f590132' (2026-04-26)
• Updated input 'nixpkgs':
    'github:nixos/nixpkgs/f937f8e' (2025-08-22)
  → 'github:nixos/nixpkgs/d233902' (2026-05-15)
• Updated input 'process-compose-flake':
    'github:Platonic-Systems/process-compose-flake/91dcc48' (2025-06-08)
  → 'github:Platonic-Systems/process-compose-flake/99bea96' (2026-01-08)
• Updated input 'services-flake':
    'github:juspay/services-flake/0a3805c' (2025-08-13)
  → 'github:juspay/services-flake/59f2ecf' (2026-05-15)

Author: github-actions[bot]