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/4e627ac2e1b8f1de7f5090064242de9a259dbbc8?narHash=sha256-lbHQ7FXGzt6/IygWvJ1lCq%2BTxcut3xYYd6VIpF1ojkg%3D' (2025-10-18)
• 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/3cbe716e2346710d6e1f7c559363d14e11c32a43?narHash=sha256-J/i5K6AAz/y5dBePHQOuzC7MbhyTOKsd/GLezSbEFiM%3D' (2025-10-16)
• Updated input 'process-compose-flake':
    'github:Platonic-Systems/process-compose-flake/91dcc48a6298e47e2441ec76df711f4e38eab94e?narHash=sha256-wJHHckWz4Gvj8HXtM5WVJzSKXAEPvskQANVoRiu2w1w%3D' (2025-06-08)
  → 'github:Platonic-Systems/process-compose-flake/e968a94633788f5d9595d727f41c2baf0714be7b?narHash=sha256-y5GSCqlGe/uZzlocCPZcjc7Gj%2BmTq7m0P6xPGx88%2BNo%3D' (2025-09-23)
• Updated input 'services-flake':
    'github:juspay/services-flake/0a3805ceced9f02254d472cc71839811fae85357?narHash=sha256-aJI3n1CO3ib6CtK1/xuUyfIZM0Lp2zdCFMsFYjjfgQo%3D' (2025-08-13)
  → 'github:juspay/services-flake/8d3ca8cb1b1208f2605447c1a1b80e379ec49e34?narHash=sha256-tTOotheH2Dr2mEkcDWjGC6CcA9tL2sGmm3vWz8kL8C0%3D' (2025-10-15)

Author: github-actions[bot]