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/52a2caecc898d0b46b2b905f058ccc5081f842da?narHash=sha256-8oNVE8TrD19ulHinjaqONf9QWCKK%2Bw4url56cdStMpM%3D' (2025-11-12)
• 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/719359f4562934ae99f5443f20aa06c2ffff91fc?narHash=sha256-b0yj6kfvO8ApcSE%2BQmA6mUfu8IYG6/uU28OFn4PaC8M%3D' (2025-10-29)
• Updated input 'nixpkgs':
    'github:nixos/nixpkgs/f937f8ecd1c70efd7e9f90ba13dfb400cf559de4?narHash=sha256-4/Jd%2BLkQ2ssw8luQVkqVs9spDBVE6h/u/hC/tzngsPo%3D' (2025-08-22)
  → 'github:nixos/nixpkgs/1d4c88323ac36805d09657d13a5273aea1b34f0c?narHash=sha256-esRhOS0APE6k40Hs/jjReXg%2Brx%2BJ5LkWw7cuWFKlwYA%3D' (2025-11-15)
• 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/08a332df554e7876260b72c3e820dd27777d84af?narHash=sha256-%2BaBOw%2BlJwkjx1R/vfpCfkYgbIpAz49YgoVnPIe9LdN0%3D' (2025-11-06)
• Updated input 'services-flake':
    'github:juspay/services-flake/0a3805ceced9f02254d472cc71839811fae85357?narHash=sha256-aJI3n1CO3ib6CtK1/xuUyfIZM0Lp2zdCFMsFYjjfgQo%3D' (2025-08-13)
  → 'github:juspay/services-flake/f21943d8bffa46708df8c7614c25491e0422f91f?narHash=sha256-rRYfRwn%2Bl74iVieVFGwfiq99yGw683rwASKQ1ljEo5w%3D' (2025-11-09)

Author: github-actions[bot]