playground typecheck fails in app/auth.config.ts due to BetterAuthClientPlugin version mismatch

[onmax]

Context

After server-side #107 work, playground still has independent client-plugin typing failures.

Reproduction

cd playground
BETTER_AUTH_SECRET=test-secret-for-testing-only-32chars npx nuxi prepare
npx vue-tsc --noEmit --pretty false

Observed

Type errors in playground/app/auth.config.ts for plugin entries (admin, passkey, multiSession, twoFactor) like:

• Type '...' is not assignable to type 'BetterAuthClientPlugin'
• Diagnostics show mixed core type versions in the same check:
  • @better-auth/core@1.5.0-beta.4
  • @better-auth/core@1.4.7

This appears to be a client/plugin-side version/type compatibility problem, separate from server defineServerAuth inference fixes.

Expected

Playground vue-tsc should typecheck app/auth.config.ts plugin list without client plugin incompatibility errors.

Scope

Separate follow-up from #107.