feat(website): Umami analytics (conversion + CTA events)

Add the Umami tracker (cookieless, no consent banner) in the document head,
limited to the production hostnames via data-domains so dev traffic doesn't
pollute the stats. Pageviews are auto-tracked per page and locale.

Custom events on the key funnel:
- demo-request (demo form submit, with teamSize)
- partner-application (partner form submit, with type)
- book-demo (every "Book a demo" CTA click) via data-umami-event
- login (clicks through to the app)

Also fix the mobile nav menu links, which weren't localized (would drop
Danish visitors back to English).

apps/website/components/landing/ComingSoon.vue

@@ -13,6 +13,6 @@ const localePath = useLocalePath()
 <template>
   <LandingPageHeader :label="copy.pages.comingSoonKicker" :title="title" :intro="body" />
   <LandingContainer pad="clamp(32px, 5vw, 48px) clamp(20px, 5vw, 64px) clamp(56px, 8vw, 160px)">
-    <LandingBtn variant="primary" size="lg" @click="navigateTo(localePath('/demo'))">{{ copy.pages.ctaDemo }} →</LandingBtn>
+    <LandingBtn variant="primary" size="lg" data-umami-event="book-demo" @click="navigateTo(localePath('/demo'))">{{ copy.pages.ctaDemo }} →</LandingBtn>
   </LandingContainer>
 </template>

apps/website/components/landing/FinalCta.vue

@@ -21,7 +21,7 @@ const localePath = useLocalePath()
       </h2>
       <div :style="{ marginTop: '28px', maxWidth: 'min(100%, 520px)', fontFamily: '\'Inter\', sans-serif', fontSize: '19px', color: 'rgba(244,243,238,0.7)' }">{{ copy.finalCta.sub }}</div>
       <div :style="{ marginTop: '40px' }">
-        <button @click="navigateTo(localePath('/demo'))" :style="{
+        <button data-umami-event="book-demo" @click="navigateTo(localePath('/demo'))" :style="{
           background: C.signal, color: C.carbon, border: 'none',
           padding: '20px 32px', fontFamily: '\'Inter\', sans-serif',
           fontSize: '16px', fontWeight: 600, borderRadius: '4px', cursor: 'pointer',

apps/website/components/landing/Hero.vue

@@ -47,7 +47,7 @@ const brush = {
       </div>
 
       <div :style="{ display: 'flex', gap: '12px', marginTop: '40px', flexWrap: 'wrap' }">
-        <LandingBtn variant="primary" size="lg" @click="navigateTo(localePath('/demo'))">{{ copy.hero.cta }} →</LandingBtn>
+        <LandingBtn variant="primary" size="lg" data-umami-event="book-demo" @click="navigateTo(localePath('/demo'))">{{ copy.hero.cta }} →</LandingBtn>
         <LandingBtn variant="secondary" size="lg">{{ copy.hero.sub_cta }}</LandingBtn>
       </div>
 

apps/website/components/landing/Nav.vue

@@ -97,8 +97,8 @@ function segStyle(code: 'en' | 'da') {
           <button :style="segStyle('en')" @click="switchTo('en')">EN</button>
           <button :style="segStyle('da')" @click="switchTo('da')">DA</button>
         </div>
-        <a :href="APP_URL" :style="{ fontFamily: '\'Inter\', sans-serif', fontSize: '14px', color: t.fgMuted }">{{ copy.nav.login }}</a>
-        <LandingBtn variant="primary" @click="navigateTo(localePath('/demo'))">{{ copy.nav.cta }} →</LandingBtn>
+        <a :href="APP_URL" data-umami-event="login" :style="{ fontFamily: '\'Inter\', sans-serif', fontSize: '14px', color: t.fgMuted }">{{ copy.nav.login }}</a>
+        <LandingBtn variant="primary" data-umami-event="book-demo" @click="navigateTo(localePath('/demo'))">{{ copy.nav.cta }} →</LandingBtn>
       </div>
 
       <!-- Hamburger — visible only on mobile via scoped CSS -->
@@ -147,7 +147,7 @@ function segStyle(code: 'en' | 'da') {
       }"
     >
       <NuxtLink
-        v-for="(it, i) in items" :key="i" :to="it.href"
+        v-for="(it, i) in items" :key="i" :to="loc(it.href)"
         :style="{
           fontFamily: '\'Inter\', sans-serif', fontSize: '16px', color: t.fgMuted,
           letterSpacing: '-0.005em', padding: '14px 0',
@@ -164,10 +164,11 @@ function segStyle(code: 'en' | 'da') {
         </div>
         <a
           :href="APP_URL"
+          data-umami-event="login"
           :style="{ fontFamily: '\'Inter\', sans-serif', fontSize: '14px', color: t.fgMuted }"
           @click="mobileOpen = false"
         >{{ copy.nav.login }}</a>
-        <LandingBtn variant="primary" @click="() => { navigateTo(localePath('/demo')); mobileOpen = false }">{{ copy.nav.cta }} →</LandingBtn>
+        <LandingBtn variant="primary" data-umami-event="book-demo" @click="() => { navigateTo(localePath('/demo')); mobileOpen = false }">{{ copy.nav.cta }} →</LandingBtn>
       </div>
     </div>
   </header>

apps/website/components/landing/Pricing.vue

@@ -18,7 +18,7 @@ const localePath = useLocalePath()
             <p :style="{ fontFamily: '\'Inter\', sans-serif', fontSize: '20px', lineHeight: 1.5, maxWidth: '640px', color: t.fgMuted, margin: 0, textWrap: 'pretty' }">{{ copy.pricing.lede }}</p>
           </div>
           <div :style="{ marginTop: '36px', display: 'flex', alignItems: 'center', gap: '16px' }">
-            <LandingBtn variant="primary" size="lg" @click="navigateTo(localePath('/demo'))">{{ copy.pricing.cta }} →</LandingBtn>
+            <LandingBtn variant="primary" size="lg" data-umami-event="book-demo" @click="navigateTo(localePath('/demo'))">{{ copy.pricing.cta }} →</LandingBtn>
           </div>
         </div>
         <div :style="{ background: t.surface, border: `1px solid ${t.border}`, borderRadius: '6px', padding: '36px 36px' }">