docs(website): tabbed per-OS install instructions with auto-detection

Split the install page into Linux / macOS / Windows tabs so each visitor
sees only the commands that apply to them. A small InstallOsDetect component
seeds Starlight's synced-tabs localStorage key with the detected OS before
the tabs render, so the matching tab is pre-selected with no flash — and
only when the visitor hasn't already picked a tab, so a manual choice wins.

- installation.md -> .mdx (needs the Tabs/TabItem components)
- detection covers navigator.userAgentData and the legacy platform/UA
  fallbacks; unknown platforms fall through to the default tab
- piggybacks on Starlight's own restore mechanism rather than re-implementing
  tab switching

website/src/components/InstallOsDetect.astro

@@ -0,0 +1,39 @@
+---
+// Pre-selects the install-instructions tab that matches the visitor's OS.
+//
+// This piggybacks on Starlight's synced-tabs mechanism rather than fighting it.
+// A `<Tabs syncKey="install-os">` restores its active tab from
+// `localStorage["starlight-synced-tabs__install-os"]` via a script Starlight
+// inlines *before* the tabs render (so there is no flash of the wrong tab). All
+// we do here is seed that same key with the detected OS — and only when the
+// visitor has not already chosen a tab themselves, so a manual choice always wins.
+//
+// Requirements (mirrors Starlight's own restore script):
+//   - Must be placed *before* the `<Tabs>` it targets, so this runs first.
+//   - The stored value must equal one of the TabItem labels exactly
+//     ("Linux" / "macOS" / "Windows").
+//   - Inlined, so it runs during parse before the restore script's
+//     connectedCallback and paint.
+---
+
+<script is:inline>
+	(() => {
+		const KEY = 'starlight-synced-tabs__install-os';
+		try {
+			// A previously stored value is a deliberate user choice — never override it.
+			if (localStorage.getItem(KEY)) return;
+			const data = navigator.userAgentData;
+			const platform = ((data && data.platform) || navigator.platform || '').toLowerCase();
+			const ua = (navigator.userAgent || '').toLowerCase();
+			let os = null;
+			if (platform.includes('win') || ua.includes('windows')) os = 'Windows';
+			else if (platform.includes('mac') || ua.includes('mac os x')) os = 'macOS';
+			else if (platform.includes('linux') || platform.includes('x11') || ua.includes('linux'))
+				os = 'Linux';
+			if (os) localStorage.setItem(KEY, os);
+		} catch (e) {
+			// localStorage unavailable (private mode, blocked cookies, …) — silently
+			// fall back to the default first tab. No detection, no harm.
+		}
+	})();
+</script>

website/src/content/docs/getting-started/installation.mdx

@@ -5,77 +5,105 @@ sidebar:
   order: 1
 ---
 
+import { Tabs, TabItem } from '@astrojs/starlight/components';
+import InstallOsDetect from '../../../components/InstallOsDetect.astro';
+
 RDBMS Playground is a single self-contained program. There is nothing to
 configure and no separate database to install — everything it needs is
 built in.
 
-Pick whichever method suits your platform. The one-line installers are the
+Pick the tab for your platform — we try to select it automatically — then
-quickest if you just want to get going.
+use whichever method you prefer. The one-line installers are the quickest if
+you just want to get going.
 
-## One line
+<InstallOsDetect />
 
-These download the matching binary for your machine, verify its checksum,
+<Tabs syncKey="install-os">
-and put it on your `PATH`.
+<TabItem label="Linux">
 
-### Linux & macOS
+**One-line installer**
 
 ```sh
 curl -fsSL https://git.lazyeval.net/oli/rdbms-playground/raw/branch/main/scripts/install.sh | sh
 ```
 
-It detects your operating system and CPU, installs to `~/.local/bin`, and
+It detects your CPU, installs to `~/.local/bin`, and prints a hint if that
-prints a hint if that directory isn't on your `PATH`. Set
+directory isn't on your `PATH`. Set `RDBMS_INSTALL_DIR` to install elsewhere,
-`RDBMS_INSTALL_DIR` to install somewhere else, or `RDBMS_VERSION=vX.Y.Z` to
+or `RDBMS_VERSION=vX.Y.Z` to pin a version. Prefer to read a script before
-pin a specific version. Prefer to read a script before running it? It lives
+running it? It lives at
-at [`scripts/install.sh`](https://git.lazyeval.net/oli/rdbms-playground/raw/branch/main/scripts/install.sh).
+[`scripts/install.sh`](https://git.lazyeval.net/oli/rdbms-playground/raw/branch/main/scripts/install.sh).
 
-### Windows (PowerShell)
+**Homebrew**
-
-```powershell
-irm https://git.lazyeval.net/oli/rdbms-playground/raw/branch/main/scripts/install.ps1 | iex
-```
-
-It downloads the matching `.exe`, verifies its checksum, installs to
-`%LOCALAPPDATA%\Programs\rdbms-playground`, and adds that folder to your
-user `PATH`. Use `-InstallDir` to choose a different location or `-Version`
-to pin a release.
-
-## Package managers
-
-### Homebrew (macOS & Linux)
 
 ```sh
 brew tap lazyeval/tap https://git.lazyeval.net/lazyeval/homebrew-tap
 brew install lazyeval/tap/rdbms-playground
 ```
 
-### Scoop (Windows)
+</TabItem>
+<TabItem label="macOS">
+
+**One-line installer**
+
+```sh
+curl -fsSL https://git.lazyeval.net/oli/rdbms-playground/raw/branch/main/scripts/install.sh | sh
+```
+
+It detects your CPU (Apple Silicon or Intel), installs to `~/.local/bin`, and
+prints a hint if that directory isn't on your `PATH`. Set `RDBMS_INSTALL_DIR`
+to install elsewhere, or `RDBMS_VERSION=vX.Y.Z` to pin a version. Prefer to
+read a script before running it? It lives at
+[`scripts/install.sh`](https://git.lazyeval.net/oli/rdbms-playground/raw/branch/main/scripts/install.sh).
+
+**Homebrew**
+
+```sh
+brew tap lazyeval/tap https://git.lazyeval.net/lazyeval/homebrew-tap
+brew install lazyeval/tap/rdbms-playground
+```
+
+</TabItem>
+<TabItem label="Windows">
+
+**One-line installer (PowerShell)**
+
+```powershell
+irm https://git.lazyeval.net/oli/rdbms-playground/raw/branch/main/scripts/install.ps1 | iex
+```
+
+It downloads the matching `.exe`, verifies its checksum, installs to
+`%LOCALAPPDATA%\Programs\rdbms-playground`, and adds that folder to your user
+`PATH`. Use `-InstallDir` to choose a different location or `-Version` to pin
+a release.
+
+**Scoop**
 
 ```sh
 scoop bucket add lazyeval https://git.lazyeval.net/lazyeval/scoop-bucket
 scoop install rdbms-playground
 ```
 
-### winget (Windows)
+**winget**
 
-:::note
 A winget package (`winget install LazyEvaluation.RdbmsPlayground`) is on its
 way and awaiting review in the public winget catalogue. Until it lands, use
 Scoop or the PowerShell one-liner above.
-:::
+
+</TabItem>
+</Tabs>
 
 ## With cargo
 
-If you have a Rust toolchain, you can install from
+These work on any platform with a Rust toolchain. Install from
 [crates.io](https://crates.io/crates/rdbms-playground):
 
 ```sh
 cargo install rdbms-playground
 ```
 
-For a faster install that fetches a prebuilt binary instead of compiling,
+For a faster install that fetches a prebuilt binary instead of compiling, use
-use [`cargo-binstall`](https://github.com/cargo-bins/cargo-binstall)
+[`cargo-binstall`](https://github.com/cargo-bins/cargo-binstall) (install it
-(install it first — it is not part of `cargo` itself):
+first — it is not part of `cargo` itself):
 
 ```sh
 cargo binstall rdbms-playground
@@ -83,11 +111,11 @@ cargo binstall rdbms-playground
 
 ## Prebuilt binaries
 
-Every release publishes static Linux, standalone Windows, and macOS
+Every release publishes static Linux, standalone Windows, and macOS binaries
-binaries (x86_64 and aarch64), each with a `.sha256` checksum, on the
+(x86_64 and aarch64), each with a `.sha256` checksum, on the
 [releases page](https://git.lazyeval.net/oli/rdbms-playground/releases).
-Download the one for your platform, make it executable if needed, and put
+Download the one for your platform, make it executable if needed, and put it
-it somewhere on your `PATH`.
+somewhere on your `PATH`.
 
 ## Run it