fix(nuxt): Optimize `@clerk/vue` #11284

Job	Run time
check-permissions	2s
Unit Tests (18)	40s
Formatting, linting & changeset checks	1m 25s
Unit Tests (22)	45s
Integration Tests (generic, chrome)	3m 40s
Integration Tests (express, chrome)	1m 59s
Integration Tests (quickstart, chrome)	1m 24s
Integration Tests (ap-flows, chrome)	1m 23s
Integration Tests (elements, chrome)	2m 44s
Integration Tests (sessions, chrome)	1m 26s
Integration Tests (astro, chrome)	1m 28s
Integration Tests (expo-web, chrome)	2m 18s
Integration Tests (tanstack-start, chrome)	1m 22s
Integration Tests (tanstack-router, chrome)	1m 23s
Integration Tests (vue, chrome)	1m 24s
Integration Tests (nuxt, chrome)	2m 22s
Integration Tests (react-router, chrome)	1m 25s
Integration Tests (nextjs, chrome, 13)	1m 25s
Integration Tests (nextjs, chrome, 14)	1m 28s
Integration Tests (nextjs, chrome, 15)	1m 29s
	31m 32s

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