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/864599284fc7c0ba6357ed89ed5e2cd5040f0c04?narHash=sha256-TmWcdiUUaWk8J4lpjzu4gCGxWY6/Ok7mOK4fIFfBuU4%3D' (2025-10-20)
• 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/02f2cb8e0feb4596d20cc52fda73ccee960e3538?narHash=sha256-tH3wHnOJms%2BU4k/rK2Nn1RfBrhffX92jLP/2VndSn0w%3D' (2025-10-24)
• 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/d1839830cd4a814830a27b3cb58437306747bbd3?narHash=sha256-l14CiQZM2ZpWp6leugJ5/GKU1aydT/xrvyKRMgYc0ak%3D' (2025-10-21)
• Updated input 'services-flake':
    'github:juspay/services-flake/0a3805ceced9f02254d472cc71839811fae85357?narHash=sha256-aJI3n1CO3ib6CtK1/xuUyfIZM0Lp2zdCFMsFYjjfgQo%3D' (2025-08-13)
  → 'github:juspay/services-flake/0d51e5da1090eb29abe722ffb73097c45e199591?narHash=sha256-uUTsSkoLOuHEcqnfocfx74c3wRJEOAP9o34DzZNRauA%3D' (2025-10-22)

Author: github-actions[bot]