Remove standalone /[locale]/chat page; enhance FloatingChat with fullscreen toggle via Launch icon; add global event to open chat (optionally fullscreen); wire home buttons/cards to open modal instead of routing.

app/[locale]/page.tsx

@@ -39,7 +39,7 @@ export default function Home() {
       title: t('features.chat.title'),
       description: t('features.chat.description'),
       icon: <Chat sx={{ fontSize: 40, color: 'secondary.main' }} />,
-      path: '/chat',
+      path: '/__open-chat__',
       color: theme.palette.secondary.main,
     },
     {
@@ -106,7 +106,9 @@ export default function Home() {
                     },
                   }}
                   startIcon={<Chat />}
-                  onClick={() => router.push(`/${locale}/chat`)}
+                  onClick={() => {
+                    window.dispatchEvent(new CustomEvent('floating-chat:open', { detail: { fullscreen: true } }))
+                  }}
                 >
                   {t('hero.cta.askAI')}
                 </Button>
@@ -152,7 +154,13 @@ export default function Home() {
                     boxShadow: 4,
                   },
                 }}
-                onClick={() => router.push(`/${locale}${feature.path}`)}
+                onClick={() => {
+                  if (feature.path === '/__open-chat__') {
+                    window.dispatchEvent(new CustomEvent('floating-chat:open', { detail: { fullscreen: true } }))
+                  } else {
+                    router.push(`/${locale}${feature.path}`)
+                  }
+                }}
               >
                 <CardContent sx={{
                   flexGrow: 1,
@@ -238,4 +246,4 @@ export default function Home() {
       </Container>
     </Box>
   )
-}
+}