chore(example/llm): Update flake.lock

Flake lock file updates:

• Updated input 'flake-parts':
    'github:hercules-ci/flake-parts/af66ad14b28a127c5c0f3bbb298218fc63528a18?narHash=sha256-pHYj8gUBapuUzKV/kN/tR3Zvqc7o6gdFB9XKXIp1SQ8%3D' (2025-08-06)
  → 'github:hercules-ci/flake-parts/4524271976b625a4a605beefd893f270620fd751?narHash=sha256-%2BuWLQZccFHwqpGqr2Yt5VsW/PbeJVTn9Dk6SHWhNRPw%3D' (2025-09-01)
• Updated input 'flake-parts/nixpkgs-lib':
    'github:nix-community/nixpkgs.lib/0f36c44e01a6129be94e3ade315a5883f0228a6e?narHash=sha256-zvaMGVn14/Zz8hnp4VWT9xVnhc8vuL3TStRqwk22biA%3D' (2025-07-27)
  → 'github:nix-community/nixpkgs.lib/a73b9c743612e4244d865a2fdee11865283c04e6?narHash=sha256-x2rJ%2BOvzq0sCMpgfgGaaqgBSwY%2BLST%2BWbZ6TytnT9Rk%3D' (2025-08-10)
• Updated input 'nixpkgs':
    'github:nixos/nixpkgs/f937f8ecd1c70efd7e9f90ba13dfb400cf559de4?narHash=sha256-4/Jd%2BLkQ2ssw8luQVkqVs9spDBVE6h/u/hC/tzngsPo%3D' (2025-08-22)
  → 'github:nixos/nixpkgs/6d7ec06d6868ac6d94c371458fc2391ded9ff13d?narHash=sha256-fEvTiU4s9lWgW7mYEU/1QUPirgkn%2BodUBTaindgiziY%3D' (2025-09-13)
• Updated input 'services-flake':
    'github:juspay/services-flake/0a3805ceced9f02254d472cc71839811fae85357?narHash=sha256-aJI3n1CO3ib6CtK1/xuUyfIZM0Lp2zdCFMsFYjjfgQo%3D' (2025-08-13)
  → 'github:juspay/services-flake/66d824d82a930afe1c961dbef686f441996cbbcf?narHash=sha256-T3nmxv6dpfJChg%2BEYVPBg3H7cpMdFbvBtLxaCtfxexc%3D' (2025-09-07)

Author: github-actions[bot]