feat(motion): pilot the universal `motion` prop on a real component (Badge) — (b) step 2

First real consumer of `motionAttrs`: `<Badge>` gains a `motion` prop so a
designer can apply any registered preset as the badge's entrance — `<Badge
motion="scale-fade">` plays the preset's enter on mount, zero per-component
machinery (the component just spreads `{...motionAttrs(motion)}`).

Badge is the clean content-domain pilot: pure eidos primitive, no morfo events,
no own `data-state` (so the helper's presentation `data-state="open"` doesn't
clash — unlike Card, which has selected/idle + a built-in emerge). Additive +
non-breaking: `motion` defaults to undefined (no animation).

- badge/types.ts: `motion?: MotionPresetName`.
- badge/badge.svelte: spread `motionAttrs(motion)` on the span.
- badge demo: a "Motion" showcase (fade / scale-fade / slide-fade + Replay) —
  the prop demonstrated per the testbed doctrine.

Verified at runtime: the three motion badges render `data-animation-style` +
`data-state="open"` with the right enter `animation-name` (fade-in / scale-in,
fade-in / slide-from-bottom, scale-in, fade-in). `check` clean for badge. (A
fresh badge screenshot was blocked by preview-infra flakiness this round; the
enter keyframes themselves were confirmed visually earlier via the cascade.)

Establishes the pattern: any component becomes animation-selectable by accepting
`motion` + spreading the helper. RFC §D.12 (b).

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

src/uix/eidos/components/badge/badge.svelte

@@ -12,7 +12,7 @@
 	 * Optional Dot / Icon / Remove sub-parts compose inside.
 	 */
 	import './badge.css';
-	import { ActiveEidos } from '$uix/eidos';
+	import { ActiveEidos, motionAttrs } from '$uix/eidos';
 	import { BADGE_LANGS } from './langs';
 	import type { BadgeProps } from './types';
 
@@ -27,6 +27,7 @@
 		onRemove,
 		removeLabel,
 		icon,
+		motion,
 		children,
 		...rest
 	}: BadgeProps = $props();
@@ -49,6 +50,7 @@
 	data-shape={shape}
 	data-dot={dot ? '' : undefined}
 	data-removable={removable ? '' : undefined}
+	{...motionAttrs(motion)}
 	{...rest}
 >
 	{#if dot}

src/uix/eidos/components/badge/types.ts

@@ -1,5 +1,6 @@
 import type { Snippet } from 'svelte';
 import type { ChipVariant, ColorRole, ResponsiveProp, ShapeFamily, Size } from '$uix/eidos/lib/types';
+import type { MotionPresetName } from '$uix/eidos/lib/motion/registry';
 import type { BoxProps } from '../box/types';
 
 /**
@@ -78,4 +79,11 @@ export type BadgeProps = Omit<BoxProps, 'display'> & {
 	icon?: Snippet;
 	/** Badge label. */
 	children?: Snippet;
+	/**
+	 * Entrance animation — any registered motion preset (`fade` / `scale-fade` /
+	 * `slide-fade` / …). The badge plays the preset's enter on mount (content
+	 * domain — RFC §D.12; routed via `motionAttrs`). `undefined` (default) = no
+	 * animation. A common use: a notification badge that pops in.
+	 */
+	motion?: MotionPresetName;
 };

web/routes/uix/components/badge/+page.svelte

@@ -30,6 +30,8 @@
 	let withIcon = $state(false);
 	let removable = $state(false);
 	let removeCount = $state(0);
+	// Remount key so the on-mount entrance animation can be replayed on demand.
+	let motionReplay = $state(0);
 
 	const variants: BadgeVariant[] = ['soft', 'solid', 'outline', 'ghost'];
 	const sizes: BadgeSize[] = ['xs', 'sm', 'md', 'lg'];
@@ -770,6 +772,31 @@
 				</Badge>
 				<Badge color="affirm" dot removable onRemove={handleRemove}>dot + remove</Badge>
 			</Box>
+
+			<div data-uix-subsection-head>Motion · entrance animation (content domain · RFC §D.12)</div>
+			<Box
+				style="display: flex; flex-direction: column; gap: var(--uix-space-3); padding: var(--uix-space-3); border: 1px solid var(--uix-border); border-radius: var(--uix-radius-md);"
+			>
+				<p style="margin: 0; color: var(--uix-muted);">
+					Any component can opt into a registered motion preset via the <code>motion</code> prop —
+					the badge plays its enter on mount (routed through <code>motionAttrs</code>, reusing the
+					existing preset, no per-component machinery). <code>undefined</code> = no animation.
+				</p>
+				<button
+					type="button"
+					onclick={() => (motionReplay += 1)}
+					style="align-self: flex-start; padding: var(--uix-space-1) var(--uix-space-3); border: 1px solid var(--uix-border); border-radius: var(--uix-radius-sm); background: var(--uix-surface); cursor: pointer;"
+				>
+					Replay ↻
+				</button>
+				{#key motionReplay}
+					<Box style="display: flex; flex-wrap: wrap; gap: var(--uix-space-3);">
+						<Badge color="primary" motion="fade">motion=&quot;fade&quot;</Badge>
+						<Badge color="affirm" motion="scale-fade">motion=&quot;scale-fade&quot;</Badge>
+						<Badge color="risk" motion="slide-fade">motion=&quot;slide-fade&quot;</Badge>
+					</Box>
+				{/key}
+			</Box>
 		</section>
 	{/if}