fix(web): keep the beta banner clear of the app shell

- render the banner through the Alert API so its grid keeps one full-width text column instead of wrapping inside the empty icon column

- point the cloud link at space.langbot.app/cloud?environment=dedicated and the self-hosted link at the GitHub repository

- keep the last known state and retry the probe (1/2/4/8s plus a re-check on window focus) so a restarting backend cannot hide the banner for the session

- publish --beta-banner-height so the fixed sidebar container, the sidebar wrapper and the wizard shell start below the banner

web/src/app/wizard/page.tsx

@@ -1061,7 +1061,10 @@ export default function WizardPage() {
 
   if (isLoading) {
     return (
-      <div className="fixed inset-0 z-50 bg-background flex items-center justify-center">
+      <div
+        style={{ top: 'var(--beta-banner-height, 0px)' }}
+        className="fixed inset-x-0 bottom-0 z-50 bg-background flex items-center justify-center"
+      >
         <LoadingSpinner text={t('wizard.loading')} />
       </div>
     );
@@ -1075,7 +1078,10 @@ export default function WizardPage() {
   ];
 
   return (
-    <div className="fixed inset-0 z-50 bg-background flex flex-col">
+    <div
+      style={{ top: 'var(--beta-banner-height, 0px)' }}
+      className="fixed inset-x-0 bottom-0 z-50 bg-background flex flex-col"
+    >
       {/* Top bar: Skip button */}
       <div className="shrink-0 flex items-center justify-between px-4 sm:px-6 py-3 border-b">
         <div className="flex items-center gap-2">

web/src/components/BetaBanner.tsx

@@ -1,80 +1,136 @@
 import { useTranslation } from 'react-i18next';
 import { AlertCircle, X } from 'lucide-react';
-import { useState, useEffect } from 'react';
+import { useState, useEffect, useRef } from 'react';
 import { Alert, AlertDescription } from '@/components/ui/alert';
 import { backendClient } from '@/app/infra/http';
 
+const RETRY_DELAYS_MS = [1000, 2000, 4000, 8000];
+const CLOUD_BETA_RETRY_LIMIT = RETRY_DELAYS_MS.length;
+
 export function BetaBanner() {
-  const { t, i18n } = useTranslation();
+  const { t } = useTranslation();
+  const bannerRef = useRef<HTMLDivElement>(null);
   const [show, setShow] = useState(false);
   const [dismissed, setDismissed] = useState(false);
+  const visible = show && !dismissed;
+
+  // Publish the banner height so the fixed app shell (sidebar + inset) starts
+  // below the notice instead of painting over it.
+  useEffect(() => {
+    const root = document.documentElement;
+    if (!visible) {
+      root.style.removeProperty('--beta-banner-height');
+      return;
+    }
+    const element = bannerRef.current;
+    if (!element) {
+      return;
+    }
+    const sync = () => {
+      root.style.setProperty(
+        '--beta-banner-height',
+        `${element.getBoundingClientRect().height}px`,
+      );
+    };
+    sync();
+    const observer = new ResizeObserver(sync);
+    observer.observe(element);
+    return () => {
+      observer.disconnect();
+      root.style.removeProperty('--beta-banner-height');
+    };
+  }, [visible]);
 
   useEffect(() => {
-    const checkBetaStatus = async () => {
+    let cancelled = false;
+    let retryTimer: number | undefined;
+
+    const checkBetaStatus = async (attempt = 0) => {
       try {
         const info = await backendClient.getSystemInfo();
-        const shouldShow =
-          info.deployment_mode === 'cloud' && info.beta === true;
-        setShow(shouldShow);
+        if (cancelled) {
+          return;
+        }
+        setShow(info.deployment_mode === 'cloud' && info.beta === true);
       } catch {
-        setShow(false);
+        if (cancelled) {
+          return;
+        }
+        // A single failed probe (cold start, restarting backend, flaky
+        // network) must not hide the banner for the rest of the session, so
+        // keep the last known state and retry with backoff.
+        if (attempt < CLOUD_BETA_RETRY_LIMIT) {
+          retryTimer = window.setTimeout(
+            () => void checkBetaStatus(attempt + 1),
+            RETRY_DELAYS_MS[attempt],
+          );
+        }
       }
     };
 
-    checkBetaStatus();
+    void checkBetaStatus();
+
+    const recheck = () => {
+      if (!cancelled) {
+        void checkBetaStatus();
+      }
+    };
+    window.addEventListener('focus', recheck);
+
+    return () => {
+      cancelled = true;
+      clearTimeout(retryTimer);
+      window.removeEventListener('focus', recheck);
+    };
   }, []);
 
-  if (!show || dismissed) {
+  if (!visible) {
     return null;
   }
 
-  const cloudUrl =
-    i18n.language === 'zh-Hans' || i18n.language === 'zh_CN'
-      ? 'https://langbot.app/zh/cloud'
-      : i18n.language === 'ja' || i18n.language === 'ja_JP'
-        ? 'https://langbot.app/ja/cloud'
-        : 'https://langbot.app/cloud';
-
-  const ossUrl =
-    i18n.language === 'zh-Hans' || i18n.language === 'zh_CN'
-      ? 'https://langbot.app/zh/docs/quick-start/deploy'
-      : i18n.language === 'ja' || i18n.language === 'ja_JP'
-        ? 'https://langbot.app/ja/docs/quick-start/deploy'
-        : 'https://langbot.app/docs/quick-start/deploy';
+  // The cloud product page opens the dedicated (paid v1) environment tab;
+  // space.langbot.app resolves the locale itself, so no path prefix applies.
+  const cloudUrl = 'https://space.langbot.app/cloud?environment=dedicated';
+  const ossUrl = 'https://github.com/langbot-app/LangBot';
 
   return (
-    <Alert className="rounded-none border-x-0 border-t-0 bg-amber-50 dark:bg-amber-950/20 border-amber-200 dark:border-amber-900/50 py-2">
-      <div className="flex items-start gap-3">
-        <AlertCircle className="h-4 w-4 mt-0.5 text-amber-600 dark:text-amber-500 shrink-0" />
-        <AlertDescription className="text-sm text-amber-900 dark:text-amber-100 flex-1">
-          {t('beta_banner.message')}{' '}
-          <a
-            href={cloudUrl}
-            target="_blank"
-            rel="noopener noreferrer"
-            className="underline hover:text-amber-700 dark:hover:text-amber-300 font-medium"
+    <Alert
+      ref={bannerRef}
+      className="relative z-30 rounded-none border-x-0 border-t-0 bg-amber-50 dark:bg-amber-950/20 border-amber-200 dark:border-amber-900/50 py-2"
+    >
+      <AlertCircle className="text-amber-600 dark:text-amber-500" />
+      <AlertDescription className="text-sm text-amber-900 dark:text-amber-100">
+        <div className="flex w-full items-start gap-3">
+          <span className="flex-1">
+            {t('beta_banner.message')}{' '}
+            <a
+              href={cloudUrl}
+              target="_blank"
+              rel="noopener noreferrer"
+              className="underline hover:text-amber-700 dark:hover:text-amber-300 font-medium"
+            >
+              {t('beta_banner.cloud_link')}
+            </a>{' '}
+            {t('beta_banner.or')}{' '}
+            <a
+              href={ossUrl}
+              target="_blank"
+              rel="noopener noreferrer"
+              className="underline hover:text-amber-700 dark:hover:text-amber-300 font-medium"
+            >
+              {t('beta_banner.oss_link')}
+            </a>
+            {t('beta_banner.period')}
+          </span>
+          <button
+            onClick={() => setDismissed(true)}
+            className="shrink-0 text-amber-600 dark:text-amber-500 hover:text-amber-800 dark:hover:text-amber-300 p-1 -mt-1 -mr-2"
+            aria-label={t('beta_banner.dismiss')}
           >
-            {t('beta_banner.cloud_link')}
-          </a>{' '}
-          {t('beta_banner.or')}{' '}
-          <a
-            href={ossUrl}
-            target="_blank"
-            rel="noopener noreferrer"
-            className="underline hover:text-amber-700 dark:hover:text-amber-300 font-medium"
-          >
-            {t('beta_banner.oss_link')}
-          </a>
-          {t('beta_banner.period')}
-        </AlertDescription>
-        <button
-          onClick={() => setDismissed(true)}
-          className="shrink-0 text-amber-600 dark:text-amber-500 hover:text-amber-800 dark:hover:text-amber-300 p-1 -mt-1 -mr-2"
-          aria-label={t('beta_banner.dismiss')}
-        >
-          <X className="h-4 w-4" />
-        </button>
-      </div>
+            <X className="h-4 w-4" />
+          </button>
+        </div>
+      </AlertDescription>
     </Alert>
   );
 }

web/src/components/ui/sidebar.tsx

@@ -203,6 +203,9 @@ function SidebarProvider({
             {
               '--sidebar-width': `${sidebarWidth}px`,
               '--sidebar-width-icon': SIDEBAR_WIDTH_ICON,
+              // Global notices (e.g. the beta banner) publish their height so
+              // the shell starts below them instead of underneath.
+              height: 'calc(100svh - var(--beta-banner-height, 0px))',
               ...style,
             } as React.CSSProperties
           }
@@ -298,6 +301,10 @@ function Sidebar({
       />
       <div
         data-slot="sidebar-container"
+        style={{
+          top: 'var(--beta-banner-height, 0px)',
+          height: 'calc(100svh - var(--beta-banner-height, 0px))',
+        }}
         className={cn(
           'fixed inset-y-0 z-10 hidden h-svh w-(--sidebar-width) transition-[left,right,width] duration-200 ease-linear md:flex',
           isSidebarResizing && 'transition-none',