site: refresh Nook demos and landing copy

[gpt-6.1-sol] The meetings, mixer and charging previews had drifted from the current app, while slogans obscured what the modules do. Match the shipped controls and behavior, reuse the existing demo machinery, and explain the landing-page features plainly without changing routing or purchase flows.

Tests: bun test src/routes/nook src/components/nook (36 passed)

NOOK-1037

src/components/nook/PhoneBeta.tsx

@@ -96,7 +96,7 @@ function CompanionDemo() {
             {allowed() ? "Allowed ✓" : "Claude Code · the-nook"}
           </p>
           <p class="text-[9px] leading-snug text-white/60">
-            {allowed() ? "Back to work." : "Run Bash: swift test"}
+            {allowed() ? "Agent running." : "Run Bash: swift test"}
           </p>
           <Show when={!allowed()}>
             <div class="mt-1.5 flex gap-1">
@@ -139,7 +139,7 @@ function CompanionDemo() {
           >
             <p class="text-[8px] font-semibold text-white/50">Codex asks</p>
             <p class="mt-0.5 text-[9.5px] leading-snug font-semibold text-white">
-              Ship it to staging?
+              Deploy to staging?
             </p>
             <div class="mt-2 space-y-1">
               <For each={["Yes", "Not yet"]}>
@@ -194,19 +194,19 @@ export default function PhoneBeta(props: { brandColor: string }) {
             TestFlight beta
           </span>
           <h2 class="text-text mb-3 text-3xl font-bold tracking-tight">
-            Your fleet, in your pocket
+            Use The Nook on iPhone and Apple Watch
           </h2>
           <p class="text-subtext0 mb-5 leading-relaxed">
-            The iPhone and Apple Watch companion is in beta. Approvals,
-            questions, and replies reach you away from the desk, and your
-            answer goes straight back to the agent.
+            The companion app is in TestFlight beta. Check your agents,
+            respond to permission requests, and answer questions when you're
+            away from your Mac.
           </p>
           <ul class="mb-8 space-y-2.5">
             <For
               each={[
                 "Allow, deny, answer, and reply from iPhone or Apple Watch",
                 "Connects over an end-to-end encrypted relay, your tailnet, or your LAN",
-                "Home Screen, Lock Screen, and watch-face widgets for fleet status",
+                "Agent status widgets for your Home Screen, Lock Screen, and watch face",
                 "Mute notifications for a while, or while you're active at the Mac"
               ]}
             >
@@ -255,7 +255,7 @@ export default function PhoneBeta(props: { brandColor: string }) {
             </form>
             <Show when={state() === "sent"}>
               <p class="text-subtext1 mt-4 text-sm">
-                Thanks. Watch your inbox for a TestFlight invite.
+                Thanks. We'll email you a TestFlight invite.
               </p>
             </Show>
             <Show when={state() === "limited"}>