feat(decks): Deck-Kategorien über den ganzen Stack

- cards-domain: DECK_CATEGORY_IDS, Labels, DeckCategorySchema,
  category-Feld im DeckSchema
- DB-Schema (decks + marketplace/decks): category-Spalte
- API-Routen: category in create/update/list/explore
- Web: DeckCategoryIcon-Komponente, Kategorie-Picker auf Deck-Detail,
  Kategorie-Icon in DeckListGrid (Marketplace)
- Layout: Bottom-Padding für floating Nav-Bar

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

packages/cards-domain/src/schemas/deck.ts

@@ -4,6 +4,37 @@ import { FsrsSettingsSchema } from './fsrs-settings.ts';
 
 const VisibilitySchema = z.enum(['private', 'space', 'public']);
 
+export const DECK_CATEGORY_IDS = [
+	'language',
+	'medicine',
+	'science',
+	'math',
+	'history',
+	'law',
+	'technology',
+	'arts',
+	'music',
+	'sport',
+	'other',
+] as const;
+
+export type DeckCategoryId = (typeof DECK_CATEGORY_IDS)[number];
+export const DeckCategorySchema = z.enum(DECK_CATEGORY_IDS);
+
+export const DECK_CATEGORY_LABELS: Record<DeckCategoryId, string> = {
+	language: 'Sprache',
+	medicine: 'Medizin',
+	science: 'Wissenschaft',
+	math: 'Mathematik',
+	history: 'Geschichte',
+	law: 'Recht',
+	technology: 'Technik',
+	arts: 'Kunst',
+	music: 'Musik',
+	sport: 'Sport',
+	other: 'Sonstiges',
+};
+
 export const DeckSchema = z
 	.object({
 		id: z.string().min(1),
@@ -15,6 +46,7 @@ export const DeckSchema = z
 			.regex(/^#[0-9a-fA-F]{6}$/)
 			.optional()
 			.nullable(),
+		category: DeckCategorySchema.optional().nullable(),
 		visibility: VisibilitySchema.default('private'),
 		fsrs_settings: FsrsSettingsSchema.default({}),
 		content_hash: z.string().optional().nullable(),
@@ -32,6 +64,7 @@ export const DeckCreateSchema = z
 			.string()
 			.regex(/^#[0-9a-fA-F]{6}$/)
 			.optional(),
+		category: DeckCategorySchema.optional(),
 		visibility: VisibilitySchema.optional(),
 		fsrs_settings: FsrsSettingsSchema.optional(),
 	})