feat(ui): migrate Mosaic Button to StyleX #31294

Job	Run time
Check Permissions	6s
Build Packages	1m 31s
Formatting \| Dedupe \| Changeset	1m 3s
Publish with pkg-pr-new	1m 39s
Bundle size	35s
Static analysis	1m 51s
Unit Tests (**)	2m 57s
Unit Tests (**)	3m 5s
Integration Tests (fastify, chrome)	1m 40s
Integration Tests (ap-flows, chrome)	3m 11s
Integration Tests (localhost, chrome)	1m 40s
Integration Tests (handshake:staging, chrome)	1m 31s
Integration Tests (express, chrome)	1m 57s
Integration Tests (nuxt, chrome)	2m 28s
Integration Tests (vue, chrome)	1m 56s
Integration Tests (react-router, chrome)	1m 53s
Integration Tests (generic, chrome)	5m 37s
Integration Tests (sessions:staging, chrome)	3m 58s
Integration Tests (tanstack-react-start, chrome)	1m 50s
Integration Tests (handshake, chrome)	1m 31s
Integration Tests (sessions, chrome)	2m 23s
Integration Tests (astro, chrome)	3m 0s
Integration Tests (hono, chrome)	1m 57s
Integration Tests (machine, chrome)	6m 19s
Integration Tests (custom, chrome)	2m 28s
Integration Tests (quickstart, chrome, 15)	2m 38s
Integration Tests (nextjs, chrome, 16)	6m 21s
Integration Tests (chrome-extension, chrome)	1m 41s
Integration Tests (billing, chrome)	5m 4s
Integration Tests (electron, chrome)	2m 0s
Integration Tests (cache-components, chrome, 16)	1m 53s
Integration Tests (nextjs, chrome, 15)	6m 46s
Integration Tests (quickstart, chrome, 16)	2m 35s
	1h 27m 4s

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