docs(readme): add install-format badges and a Nix flake section (#949)

Represent every distribution format in the README header shields:
AppImage, .deb, .rpm, Flatpak, Snap (edge), AUR, PyPI, and Nix flake,
grouped on their own row above the social badges. Also documents the
flake install path in the Install section.

Co-authored-by: Jatin K Malik <jatinkrmalik@gmail.com>

README.md

@@ -18,12 +18,19 @@
 [![Python 3.11+](https://img.shields.io/badge/python-3.11+-blue.svg)](https://www.python.org/downloads/)
 [![PRs Welcome](https://img.shields.io/badge/PRs-welcome-brightgreen.svg)](CONTRIBUTING.md)
 
+[![GitHub release](https://img.shields.io/github/v/release/VocaHQ/vocalinux)](https://github.com/VocaHQ/vocalinux/releases)
+[![AppImage](https://img.shields.io/badge/AppImage-x86__64%20%7C%20aarch64-2C5BB4)](https://github.com/VocaHQ/vocalinux/releases/latest)
+[![.deb](https://img.shields.io/badge/.deb-Debian%20%7C%20Ubuntu-A81D33?logo=debian&logoColor=white)](https://github.com/VocaHQ/vocalinux/releases/latest)
+[![.rpm](https://img.shields.io/badge/.rpm-Fedora-EE0000?logo=fedora&logoColor=white)](https://github.com/VocaHQ/vocalinux/releases/latest)
+[![Flatpak](https://img.shields.io/badge/Flatpak-vocahq%20remote-4A90D9?logo=flatpak&logoColor=white)](#flatpak-any-distro)
+[![Snap](https://img.shields.io/badge/Snap-edge-82BEA0?logo=snapcraft&logoColor=white)](https://snapcraft.io/vocalinux)
+[![AUR](https://img.shields.io/aur/version/vocalinux)](https://aur.archlinux.org/packages/vocalinux)
+[![PyPI](https://img.shields.io/pypi/v/vocalinux)](https://pypi.org/project/vocalinux/)
+[![Nix flake](https://img.shields.io/badge/Nix-flake-5277C3?logo=nixos&logoColor=white)](packaging/nix/README.md)
+
 [![Discord](https://img.shields.io/discord/1538633755877580810?logo=discord&logoColor=white&label=Discord)](https://discord.gg/t6muquAJbm)
 [![VocaHQ](https://img.shields.io/badge/VocaHQ-vocahq.com-1a7f4e)](https://vocahq.com)
 [![Follow on X](https://img.shields.io/badge/Follow%20%40vocahq-000000?style=flat&logo=x&logoColor=white)](https://x.com/vocahq)
-[![GitHub release](https://img.shields.io/github/v/release/VocaHQ/vocalinux)](https://github.com/VocaHQ/vocalinux/releases)
-[![PyPI](https://img.shields.io/pypi/v/vocalinux)](https://pypi.org/project/vocalinux/)
-[![AUR](https://img.shields.io/aur/version/vocalinux)](https://aur.archlinux.org/packages/vocalinux)
 
 [Website](https://vocalinux.com) · [Install](#install) · [Docs](#documentation) · [Releases](https://github.com/VocaHQ/vocalinux/releases)
 
@@ -44,7 +51,7 @@ No Voca account is required. Models download once. After that, speech-to-text st
 - **Toggle or push-to-talk**: New installs default to hold Right Alt; existing configs keep their shortcut
 - **System tray + settings**: Searchable sidebar, Speech Model simple setup with Advanced as an island, status icons, audio feedback
 - **Start on login**: XDG autostart (desktop session, not a systemd service)
-- **Packaging**: install script, `.deb` / `.rpm`, AppImage, AUR, PyPI, Snap (`--edge`), Flatpak (release bundles and local build; not on Flathub)
+- **Packaging**: install script, `.deb` / `.rpm`, AppImage, AUR, PyPI, Snap (`--edge`), Flatpak (release bundles and local build; not on Flathub), Nix flake
 
 ## Screenshots
 
@@ -222,6 +229,15 @@ sudo snap install --dangerous ./vocalinux_0.18.2_amd64.snap
 sudo snap connect vocalinux:uinput
 ```
 
+### Nix / NixOS (flake)
+
+```bash
+nix run github:VocaHQ/vocalinux          # try it
+nix profile install github:VocaHQ/vocalinux
+```
+
+The flake also ships `nixosModules.vocalinux` and `homeManagerModules.vocalinux` for declarative installs (`programs.vocalinux.enable = true`). The bundled pywhispercpp builds with Vulkan GPU inference. Details: [packaging/nix/README.md](packaging/nix/README.md).
+
 ### From source
 
 ```bash
@@ -318,7 +334,7 @@ Neural VAD (Silero) is used when `onnxruntime` is available; install via `pip in
 
 | Document | Description |
 |----------|-------------|
-| [Installation](docs/INSTALL.md) | Installer, AppImage, AUR, Flatpak, Snap, running |
+| [Installation](docs/INSTALL.md) | Installer, AppImage, AUR, Flatpak, Snap, Nix flake, running |
 | [Manual / PyPI install](docs/INSTALL_MANUAL.md) | Package lists and pip workflows |
 | [Troubleshooting](docs/TROUBLESHOOTING.md) | Common failures |
 | [User guide](docs/USER_GUIDE.md) | Dictation, engines, models, tips |