Add likes, follows and playlist visibility; redesign web-player UI

Backend:
- New Likes feature (toggle/get liked tracks) and endpoints
- User follow/unfollow, listening stats, public user profile
- Playlist visibility (public/private) support
- Various auth and DTO/response adjustments to support the above

Frontend (web-player):
- New design system pass: theme tokens/mode (light/dark), glass menu,
  tabs bar, player dock/extras/queue components, mix tiles, artist link
- New routes: Liked, public user profile (/u/[id]), likes API proxy
- Search refactor: shared SearchBox component used by TopBar and
  MobileHeader (search now reachable on mobile), live results as you
  type instead of requiring Enter, dropped the "Buscando…" quick-result
  preview
- Removed now-unused components (MobileNav, CoverBadge, MixBentoTile,
  PlayPauseOverlay, SuggestionsTable, userDirectory)
- Design handoff reference docs added under web-player/design_handoff_musify_player
  and web-player/docs/design-system-refactor-plan.md

web-player/src/lib/components/ui/MixTile.svelte

@@ -0,0 +1,51 @@
+<script lang="ts">
+	import Play from '@lucide/svelte/icons/play';
+	import MixArt from './MixArt.svelte';
+	import { player } from '$lib/player/player.svelte';
+	import { queueItemForTarget } from '$lib/tracks';
+	import { mixItemTarget, type Mix } from '$lib/mixes';
+
+	interface Props {
+		mix: Mix;
+		index?: number;
+		class?: string;
+	}
+
+	let { mix, index = 0, class: klass = '' }: Props = $props();
+
+	function play(event: MouseEvent) {
+		event.preventDefault();
+		const items = mix.items.map((item) => queueItemForTarget(mixItemTarget(item)));
+		player.playQueue(items, 0);
+	}
+</script>
+
+<a
+	href="/mixes/{mix.id}"
+	class="group/tile animate-enter block cursor-pointer {klass}"
+	style="animation-delay:{Math.min(index, 10) * 45}ms"
+>
+	<div class="relative aspect-square overflow-hidden rounded-art shadow-art">
+		<MixArt
+			items={mix.items}
+			class="h-full w-full scale-100 transition duration-300 group-hover/tile:scale-105"
+		/>
+		<div
+			class="pointer-events-none absolute inset-0 bg-linear-to-b from-transparent from-45% to-black/42"
+		></div>
+		<button
+			type="button"
+			onclick={play}
+			aria-label="Reproducir {mix.title}"
+			class="absolute right-2.5 bottom-2.5 grid h-9.5 w-9.5 place-items-center rounded-full border border-white/12 bg-ink/76 text-fg opacity-0 backdrop-blur-[8px] transition-opacity duration-150 group-hover/tile:opacity-100"
+		>
+			<Play class="h-3.5 w-3.5" fill="currentColor" />
+		</button>
+	</div>
+	<div class="mt-3.25 truncate text-[13px] font-semibold tracking-[-0.01em] text-fg">
+		{mix.title}
+	</div>
+	{#if mix.subtitle}
+		<div class="mt-1 truncate text-[11.5px] text-fg-3">{mix.subtitle}</div>
+	{/if}
+</a>