fix(examples): use auth-ui imports

[thekauer]

Problem

Bug bash found example apps importing the deprecated compatibility CSS path @neondatabase/auth/ui/tailwind, which can fail to resolve. Current Neon Auth UI docs prefer direct imports from @neondatabase/auth-ui.

Summary of changes

• Migrated affected example CSS, component, and server-helper imports to @neondatabase/auth-ui / @neondatabase/auth-ui/server.
• Added @neondatabase/auth-ui as a workspace:* dependency to affected example packages and refreshed pnpm-lock.yaml.
• Updated example docs and Neon Auth setup guidance to avoid deprecated compatibility UI imports.

Refs:
#0000

Verification steps

• pnpm install --lockfile-only
• pnpm install --frozen-lockfile
• pnpm --filter neon-todo run build
• NEON_AUTH_BASE_URL=https://ep-xxx.neonauth.us-east-1.aws.neon.tech/neondb/auth NEON_AUTH_COOKIE_SECRET=REPLACE_WITH_RANDOM_SECRET_AT_LEAST_32_CHARS DATABASE_URL=postgresql://neondb_owner:password@ep-xxx.us-east-1.aws.neon.tech/neondb?sslmode=require pnpm --filter neon-auth-netxtjs run build
• pnpm --filter neon-auth-netxtjs run lint
• pnpm --filter nextjs-phone-login run build reaches TypeScript, then fails on an existing components/phone-login-form.tsx sessionUser?.phoneNumber type error unrelated to this import migration.
• pnpm --filter neon-auth-magic-link-example run build reaches TypeScript, then fails on an existing components/magic-link-form.tsx authClient.signIn.magicLink type error unrelated to this import migration.
• pnpm --filter neon-auth-magic-link-example run lint and pnpm --filter neon-todo run lint fail on existing React Hooks / no-explicit-any lint issues outside the changed import paths.
• pnpm --filter nextjs-phone-login run lint is blocked because the package script runs next lint, which Next 16 treats as an invalid project directory; direct eslint also fails on the existing ESLint config circular-reference error.

[vercel]

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Project	Deployment	Actions	Updated (UTC)
neon-auth-nextjs	Ready	Preview, Comment	Jun 30, 2026 1:27pm
react-neon-js	Ready	Preview, Comment	Jun 30, 2026 1:27pm

2 Skipped Deployments

Project	Deployment	Actions	Updated (UTC)
neon-auth-magic-link-example	Ignored	Preview	Jun 30, 2026 1:27pm
react-auth-external-ui	Ignored		Jun 30, 2026 1:27pm