docs: Add component specification and usage examples for N8nBadge

packages/frontend/@n8n/design-system/src/v2/components/Badge/component-badge.md

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+# Component specification
+
+Displays short text or icons to represent status, categories, or counts. Badges help users quickly identify important information through visual indicators without cluttering the interface.
+
+- **Component Name:** N8nBadge
+- **Figma Component:** TBD
+- **Current Implementation:** Custom component (no Element+ dependency)
+- **Reka UI Component:** N/A (Reka UI does not provide a Badge primitive)
+- **Nuxt UI Reference:** [Badge](https://ui.nuxt.com/docs/components/badge) (custom implementation, not based on Reka UI)
+
+## Public API Definition
+
+**Props**
+
+- `theme?: BadgeTheme` - Visual style variant for the badge. Values: `'default' | 'success' | 'warning' | 'danger' | 'primary' | 'secondary' | 'tertiary'`. Default: `'default'`
+  - `default`: Subtle border badge with neutral styling
+  - `success`: Green indicator for positive states
+  - `warning`: Yellow/orange indicator for cautionary states
+  - `danger`: Red indicator for error/critical states
+  - `primary`: Filled badge with contrasting text (pill-shaped)
+  - `secondary`: Filled badge with tinted background
+  - `tertiary`: Minimal badge variant with reduced padding
+- `size?: TextSize` - Size of the badge text. Values: `'xsmall' | 'small' | 'mini' | 'medium' | 'large' | 'xlarge'`. Default: `'small'`
+- `bold?: boolean` - Whether to render text in bold weight. Default: `false`
+- `showBorder?: boolean` - Whether to show the badge border. Default: `true`
+
+**Slots**
+
+- `default` - Badge content (text, icons, or mixed content). Wrapped in N8nText component for consistent typography.
+
+### Template usage examples
+
+**Simple text badge:**
+```typescript
+<script setup lang="ts">
+import { N8nBadge } from '@n8n/design-system'
+</script>
+
+<template>
+  <N8nBadge theme="default">
+    Read Only
+  </N8nBadge>
+</template>
+```
+
+**Status indicators:**
+```typescript
+<script setup lang="ts">
+import { N8nBadge } from '@n8n/design-system'
+import { computed } from 'vue'
+
+const status = ref<'success' | 'warning' | 'danger'>('success')
+
+const statusTheme = computed(() => {
+  const themeMap = {
+    success: 'success',
+    warning: 'warning',
+    danger: 'danger',
+  }
+  return themeMap[status.value]
+})
+</script>
+
+<template>
+  <N8nBadge :theme="statusTheme">
+    {{ status }}
+  </N8nBadge>
+</template>
+```
+
+**Count badge (primary theme):**
+```typescript
+<script setup lang="ts">
+import { N8nBadge } from '@n8n/design-system'
+
+const filterCount = ref(5)
+</script>
+
+<template>
+  <N8nBadge theme="primary">
+    {{ filterCount }}
+  </N8nBadge>
+</template>
+```
+
+**Tertiary minimal label:**
+```typescript
+<script setup lang="ts">
+import { N8nBadge } from '@n8n/design-system'
+</script>
+
+<template>
+  <N8nBadge theme="tertiary" :bold="true">
+    Pending
+  </N8nBadge>
+</template>
+```
+
+**Badge with icon and text:**
+```typescript
+<script setup lang="ts">
+import { N8nBadge } from '@n8n/design-system'
+import ProjectIcon from './ProjectIcon.vue'
+
+const projectBadge = {
+  icon: 'project',
+  text: 'Team Project'
+}
+</script>
+
+<template>
+  <N8nBadge
+    theme="tertiary"
+    :show-border="false"
+  >
+    <ProjectIcon :icon="projectBadge.icon" size="mini" />
+    <span>{{ projectBadge.text }}</span>
+  </N8nBadge>
+</template>
+```
+
+**Multiple sizes:**
+```typescript
+<script setup lang="ts">
+import { N8nBadge } from '@n8n/design-system'
+</script>
+
+<template>
+  <N8nBadge theme="primary" size="xsmall">XS</N8nBadge>
+  <N8nBadge theme="primary" size="small">Small</N8nBadge>
+  <N8nBadge theme="primary" size="medium">Medium</N8nBadge>
+</template>
+```
+
+**With custom CSS classes:**
+```typescript
+<script setup lang="ts">
+import { N8nBadge } from '@n8n/design-system'
+</script>
+
+<template>
+  <N8nBadge class="ml-3xs" theme="warning" :bold="true">
+    Action Required
+  </N8nBadge>
+</template>
+```
+
+**Conditional rendering:**
+```typescript
+<script setup lang="ts">
+import { N8nBadge } from '@n8n/design-system'
+
+const isReadOnly = ref(true)
+const needsSetup = ref(false)
+</script>
+
+<template>
+  <N8nBadge v-if="isReadOnly" theme="tertiary" :bold="true">
+    Read Only
+  </N8nBadge>
+
+  <N8nBadge v-if="needsSetup" theme="warning">
+    Setup Required
+  </N8nBadge>
+</template>
+```
+
+**With inline styles (advanced):**
+```typescript
+<script setup lang="ts">
+import { N8nBadge } from '@n8n/design-system'
+</script>
+
+<template>
+  <N8nBadge
+    theme="warning"
+    style="height: 25px"
+  >
+    Custom Height
+  </N8nBadge>
+</template>
+```
+
+**Dynamic theme binding:**
+```typescript
+<script setup lang="ts">
+import { N8nBadge } from '@n8n/design-system'
+import type { BadgeTheme } from '@n8n/design-system/types'
+
+interface FileStatus {
+  status: 'completed' | 'pending' | 'failed'
+}
+
+const file = ref<FileStatus>({ status: 'completed' })
+
+const getStatusTheme = (status: string): BadgeTheme => {
+  const themeMap: Record<string, BadgeTheme> = {
+    completed: 'success',
+    pending: 'warning',
+    failed: 'danger',
+  }
+  return themeMap[status] || 'default'
+}
+
+const statusLabel = (status: string) => {
+  const labelMap: Record<string, string> = {
+    completed: 'Completed',
+    pending: 'Pending',
+    failed: 'Failed',
+  }
+  return labelMap[status] || status
+}
+</script>
+
+<template>
+  <N8nBadge :theme="getStatusTheme(file.status)">
+    {{ statusLabel(file.status) }}
+  </N8nBadge>
+</template>
+```