Add development environment instructions for NixOS

[polyfloyd]

Proposed change

Adds some instructions to set up the development environment on NixOS.

Type of change

• Document existing features within Home Assistant
• Document new or changing features for which there is an existing pull request elsewhere
• Spelling or grammatical corrections, or rewording for improved clarity
• Changes to the backend of this documentation
• Remove stale or deprecated documentation

Checklist

• I have read and followed the documentation guidelines.
• I have verified that my changes render correctly in the documentation.

Additional information

• This PR fixes or closes issue: fixes #
• Link to relevant existing code or pull request:

Summary by CodeRabbit

• Documentation
  • Added instructions for setting up a development environment on NixOS, including a complete Nix configuration file with all necessary dependencies for local development.

[coderabbitai]

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ℹ️ Review info

⚙️ Run configuration

Configuration used: Organization UI

Review profile: CHILL

Plan: Pro

Run ID: 25c55939-df4e-4c0b-bc28-b378ec796369

📥 Commits

Reviewing files that changed from the base of the PR and between 8294266 and bb57428.

📒 Files selected for processing (1)

• docs/development_environment.mdx

📝 Walkthrough

Walkthrough

Added a new "Developing on NixOS" section to the development environment documentation, providing instructions to configure a Nix development shell with required dependencies (autoconf, clang, cmake, ffmpeg, python3.14, and other libraries) and environment variable settings for development on NixOS systems.

Changes

Cohort / File(s)	Summary
NixOS Development Setup Documentation docs/development_environment.mdx	Added "Developing on NixOS" section with default.nix configuration instructions, listing development dependencies and LD_LIBRARY_PATH setup.

Estimated code review effort

🎯 1 (Trivial) | ⏱️ ~3 minutes

🚥 Pre-merge checks | ✅ 3

✅ Passed checks (3 passed)

Check name	Status	Explanation
Title check	✅ Passed	The title clearly and specifically describes the main change: adding NixOS development environment setup instructions.
Description check	✅ Passed	The description follows the template structure with all required sections completed: proposed change, type of change checkbox selected, and checklist items marked.
Docstring Coverage	✅ Passed	No functions found in the changed files to evaluate docstring coverage. Skipping docstring coverage check.

_{✏️ Tip: You can configure your own custom pre-merge checks in the settings.}

✨ Finishing Touches

🧪 Generate unit tests (beta)

• Create PR with unit tests

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[coderabbitai]

Actionable comments posted: 1

🤖 Prompt for all review comments with AI agents

Verify each finding against the current code and only fix it if needed.

Inline comments:
In `@docs/development_environment.mdx`:
- Around line 114-115: Rewrite the sentence containing "Drop a `default.nix`..."
to remove the duplicated "with" and make it goal-first and authoritative: start
with the goal (e.g., "To activate a Nix environment, ..."), then give the step
("drop a `default.nix` with the contents below into the repository") and finish
with the activation method ("activate the environment, e.g., using direnv").
Ensure the phrasing is direct and imperative, removes the duplicate "with with",
and keeps the example reference to direnv.

🪄 Autofix (Beta)

Fix all unresolved CodeRabbit comments on this PR:

• Push a commit to this branch (recommended)
• Create a new PR with the fixes

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ℹ️ Review info

⚙️ Run configuration

Configuration used: Organization UI

Review profile: CHILL

Plan: Pro

Run ID: 867a5476-dcd7-4125-8e98-08890c02d925

📥 Commits

Reviewing files that changed from the base of the PR and between 0ca211d and 8294266.

📒 Files selected for processing (1)

• docs/development_environment.mdx