[skills] Sync auth with current docs (#316)

* [skills] Sync auth with current docs

<!-- vercel-plugin-drift-agent -->

* [skills] Correct Clerk Core 3 minimum Next.js version

@clerk/nextjs v7 peers on next ^15.2.8 || ^15.3.8 || ^15.4.10 || ^15.5.9 ||
^16.0.10, and Clerk corrected its upgrade guidance (clerk/javascript#9790).

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Co-authored-by: vercel-gh-bot-2[bot] <282331341+vercel-gh-bot-2[bot]@users.noreply.github.com>
Co-authored-by: molebox <rich@vercel.com>

Author: 3 people

skills/auth/SKILL.md

@@ -468,7 +468,7 @@ Server plugin + matching client plugin + re-run migrations.
 | Passkeys (WebAuthn) | `passkey` from `@better-auth/passkey` | `passkeyClient` |
 | Enterprise SSO (SAML/OIDC) | `sso` from `@better-auth/sso` | — |
 | Stripe subscriptions | `stripe` from `@better-auth/stripe` | `stripeClient` |
-| Third-party tokens via Vercel Connect | `genericOAuth` + `connect` from `@vercel/connect/betterauth` | — |
+| Sign in through a Vercel Connect connector | `genericOAuth` from `better-auth/plugins/generic-oauth` + `connect` from `@vercel/connect/betterauth` | — (v1.7 signs in with `authClient.signIn.social`; `genericOAuthClient` only exists on v1.6 and earlier) |
 
 ### Agent Tooling
 
@@ -642,7 +642,7 @@ Clerk provides an upgrade CLI that scans your codebase and applies codemods: `np
 - **`ClerkProvider` must be inside `<body>`, not wrapping `<html>`** — the CLI handles this automatically
 - **`@clerk/types` removed** — import types from the SDK's own `/types` entry point, or `@clerk/shared/types` for framework-agnostic code
 - **Redirect props renamed** — `afterSignInUrl`/`afterSignUpUrl`/`redirectUrl` → `fallbackRedirectUrl`/`signUpFallbackRedirectUrl`/`forceRedirectUrl`
-- **Minimum Next.js version: 15.2.3** — Next.js 13 and 14 are no longer supported
+- **Minimum Next.js version: 15.2.8 (or 16.0.10 on Next.js 16)** — later 15.x minors need their patched releases too (15.3.8+, 15.4.10+, 15.5.9+); Next.js 13 and 14 are no longer supported
 - **Satellite domains** — apps no longer auto-redirect on first visit; set `satelliteAutoSync: true` in middleware and `ClerkProvider` to restore Core 2 behavior
 - **`getToken()` throws `ClerkOfflineError` when offline** — previously returned `null`; still returns `null` when signed out
 
@@ -653,7 +653,7 @@ Clerk provides an upgrade CLI that scans your codebase and applies codemods: `np
 - **Accessing protected deployments from CLI or tests** → `⤳ skill: access-protected-vercel-deployment`
 - **Environment variable management** → `⤳ skill: env-vars`
 - **Neon Postgres / Upstash Redis for Better Auth** → `⤳ skill: vercel-storage`
-- **Third-party OAuth tokens through Better Auth (`@vercel/connect/betterauth`)** → `⤳ skill: vercel-connect`
+- **Sign-in through a Vercel Connect connector with Better Auth (`@vercel/connect/betterauth`); provider API tokens use `getToken()`** → `⤳ skill: vercel-connect`
 
 ## Official Documentation