feat(frontend): live unseen alerts badge on the menu button and in settings

frontend/src/lib/components/MainMenu.svelte

@@ -1,5 +1,6 @@
 <script lang="ts">
   import { DropdownMenu } from "bits-ui";
+  import AlertBadge from "#lib/components/alerts/AlertBadge.svelte";
   import AccountAvatar from "#lib/components/settings/AccountAvatar.svelte";
   import AddAccountDialog from "#lib/components/settings/AddAccountDialog.svelte";
   import Button from "#lib/components/ui/Button.svelte";
@@ -50,6 +51,7 @@
     {#snippet child({
       props,
     })}
+      <span class="menu-trigger">
         <Button
           {...props}
           aria-label={t("menu.open")}
@@ -59,6 +61,8 @@
         >
           <Icon name="menu" />
         </Button>
+        <AlertBadge />
+      </span>
     {/snippet}
   </DropdownMenu.Trigger>
   <DropdownMenu.Portal>
@@ -105,7 +109,12 @@
           onSelect={() => ui.openPanel(entry.panel)}
         >
           <Icon name={entry.icon} size="1.125rem" />
+          {#if entry.panel === "alerts"}
+            <span class="account-name">{t(entry.label)}</span>
+            <AlertBadge inline />
+          {:else}
             {t(entry.label)}
+          {/if}
         </DropdownMenu.Item>
       {/each}
       <DropdownMenu.Separator class="bg-menu-separator" />
@@ -127,6 +136,12 @@
 <AddAccountDialog bind:open={adding} />
 
 <style lang="scss">
+  .menu-trigger {
+    position: relative;
+    display: flex;
+    flex-shrink: 0;
+  }
+
   :global(.main-menu) {
     width: 17rem;
     max-height: calc(100dvh - 5rem);

frontend/src/lib/components/alerts/AlertBadge.svelte

@@ -0,0 +1,65 @@
+<script lang="ts">
+  import { t } from "#lib/i18n/locale.svelte.js";
+  import { accounts } from "#lib/stores/accounts.svelte.js";
+  import { alerts } from "#lib/stores/alerts.svelte.js";
+
+  interface Props {
+    inline?: boolean;
+  }
+
+  const { inline = false }: Props = $props();
+
+  const MAX_SHOWN = 99;
+
+  const count = $derived(alerts.unseen);
+
+  $effect(() => {
+    alerts.track(accounts.selectedId);
+  });
+</script>
+
+{#if count > 0}
+  <span class="alert-badge" title={t("alerts.badge", { count })} class:inline>
+    {count > MAX_SHOWN ? `${MAX_SHOWN}+` : count}
+  </span>
+{/if}
+
+<style lang="scss">
+  .alert-badge {
+    pointer-events: none;
+
+    position: absolute;
+    top: 0;
+    right: -0.125rem;
+
+    min-width: 1.125rem;
+    height: 1.125rem;
+    padding: 0 0.3125rem;
+    border-radius: 0.5625rem;
+
+    font-size: 0.6875rem;
+    font-weight: var(--font-weight-medium);
+    font-variant-numeric: tabular-nums;
+    line-height: 1.125rem;
+    color: var(--color-white);
+    text-align: center;
+
+    background-color: var(--color-primary);
+    box-shadow: 0 0 0 2px var(--color-background);
+
+    &.inline {
+      position: static;
+      flex-shrink: 0;
+
+      min-width: 1.375rem;
+      height: 1.375rem;
+      padding: 0 0.4375rem;
+      border-radius: 0.6875rem;
+
+      font-size: 0.8125rem;
+      line-height: 1.375rem;
+
+      box-shadow: none;
+    }
+  }
+</style>

frontend/src/lib/components/settings/Settings.svelte

@@ -1,4 +1,5 @@
 <script lang="ts">
+  import AlertBadge from "#lib/components/alerts/AlertBadge.svelte";
   import About from "#lib/components/settings/About.svelte";
   import Appearance from "#lib/components/settings/Appearance.svelte";
   import Language from "#lib/components/settings/Language.svelte";
@@ -77,7 +78,11 @@
         icon="unmute"
         label={t("settings.alerts")}
         onclick={() => ui.openPanel("alerts")}
-      />
+      >
+        {#snippet trailing()}
+          <AlertBadge inline />
+        {/snippet}
+      </SettingsItem>
     </div>
 
     <About />

frontend/src/lib/components/settings/SettingsItem.svelte

@@ -1,4 +1,5 @@
 <script lang="ts">
+  import type { Snippet } from "svelte";
   import { ripple } from "#lib/actions/ripple.js";
   import Icon from "#lib/components/ui/Icon.svelte";
 
@@ -6,10 +7,11 @@
     icon: string;
     label: string;
     onclick?: () => void;
+    trailing?: Snippet;
     value?: string;
   }
 
-  let { icon, label, value, onclick }: Props = $props();
+  let { icon, label, value, onclick, trailing }: Props = $props();
 </script>
 
 <button class="settings-item" {onclick} type="button" use:ripple>
@@ -18,6 +20,7 @@
   {#if value}
     <span class="value">{value}</span>
   {/if}
+  {@render trailing?.()}
   {#if onclick}
     <Icon class="chevron" name="arrow-right" size="1rem" />
   {/if}

frontend/src/routes/app/+layout.svelte

@@ -1,5 +1,5 @@
 <script lang="ts">
-  import { untrack } from "svelte";
+  import { onMount, untrack } from "svelte";
   import { cubicOut } from "svelte/easing";
   import { fly } from "svelte/transition";
   import ChatList from "#lib/components/ChatList.svelte";
@@ -15,6 +15,7 @@
   import Icon from "#lib/components/ui/Icon.svelte";
   import { t } from "#lib/i18n/locale.svelte.js";
   import { accounts } from "#lib/stores/accounts.svelte.js";
+  import { ALERTS_PARAM } from "#lib/stores/alerts.svelte.js";
   import { auth } from "#lib/stores/auth.svelte.js";
   import { events } from "#lib/stores/events.svelte.js";
   import { search } from "#lib/stores/search.svelte.js";
@@ -56,6 +57,12 @@
       search.close();
     });
   });
+
+  onMount(() => {
+    if (page.url.searchParams.has(ALERTS_PARAM)) {
+      ui.openPanel("alerts");
+    }
+  });
 </script>
 
 <div