Release v3.16.0 (#1769)

* Prepare release v3.16.0

* Update test fixtures with the new nix-installer version

* Update Determinate Nix release to 3.16.0

* flake.lock: Update

Flake lock file updates:

• Updated input 'determinate':
    'https://api.flakehub.com/f/pinned/DeterminateSystems/determinate/3.15.2/019bde7d-0725-73ef-9705-498c50ef6e00/source.tar.gz' (2026-01-21)
  → 'https://api.flakehub.com/f/pinned/DeterminateSystems/determinate/3.16.0/019c58b5-64dc-77f9-b913-8738b7d338cc/source.tar.gz' (2026-02-13)
• Updated input 'determinate/determinate-nixd-aarch64-darwin':
    'https://install.determinate.systems/determinate-nixd/tag/v3.15.2/macOS'
  → 'https://install.determinate.systems/determinate-nixd/tag/v3.16.0/macOS'
• Updated input 'determinate/determinate-nixd-aarch64-linux':
    'https://install.determinate.systems/determinate-nixd/tag/v3.15.2/aarch64-linux'
  → 'https://install.determinate.systems/determinate-nixd/tag/v3.16.0/aarch64-linux'
• Updated input 'determinate/determinate-nixd-x86_64-linux':
    'https://install.determinate.systems/determinate-nixd/tag/v3.15.2/x86_64-linux'
  → 'https://install.determinate.systems/determinate-nixd/tag/v3.16.0/x86_64-linux'
• Updated input 'nix':
    'https://api.flakehub.com/f/pinned/DeterminateSystems/nix-src/3.15.2/019bde75-b4ee-74b2-a812-28dc2ee83d58/source.tar.gz' (2026-01-21)
  → 'https://api.flakehub.com/f/pinned/DeterminateSystems/nix-src/3.16.0/019c589d-45e9-7337-9ff0-a8d78fecf63f/source.tar.gz' (2026-02-13)
• Updated input 'nixpkgs':
    'https://api.flakehub.com/f/pinned/NixOS/nixpkgs/0.1.928726%2Brev-e4bae1bd10c9c57b2cf517953ab70060a828ee6f/019bc8c9-d277-7e35-b3d9-c36e1fdbfb5a/source.tar.gz' (2026-01-16)
  → 'https://api.flakehub.com/f/pinned/NixOS/nixpkgs/0.1.944744%2Brev-ec7c70d12ce2fc37cb92aff673dcdca89d187bae/019c5479-7aec-77e1-8c91-c2c6a5fd4d29/source.tar.gz' (2026-02-11)

* Update Cargo dependencies

* Set Cargo.toml package.version to 3.16.0

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Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>

Author: github-actions[bot]