[Backport release-25.11] nixos/qui: init service

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Automatic backport of #472934 failed because of a merge conflict in the release notes. This PR cherry picks the commits from the original PR and fixes the merge conflict.

Additionally, the default cherry pick doesn't put qui in the right place in the module list. This is also fixed.

Things done

• Built on platform:
  • x86_64-linux
  • aarch64-linux
  • x86_64-darwin
  • aarch64-darwin
• Tested, as applicable:
  • NixOS tests in nixos/tests.
  • Package tests at passthru.tests.
  • Tests in lib/tests or pkgs/test for functions and "core" functionality.
• Ran nixpkgs-review on this PR. See nixpkgs-review usage.
• Tested basic functionality of all binary files, usually in ./result/bin/.
• Nixpkgs Release Notes
  • Package update: when the change is major or breaking.
• NixOS Release Notes
  • Module addition: when adding a new NixOS module.
  • Module update: when the change is significant.
• Fits CONTRIBUTING.md, pkgs/README.md, maintainers/README.md and other READMEs.

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nixpkgs-review result

Generated using nixpkgs-review.

Command: nixpkgs-review pr 483956 --package nixosTests.qui
Commit: eddbe6c34fd1bee1e9ddd7ff154f12e07f8c394d

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x86_64-linux

✅ 1 test built:

• nixosTests.qui