docs(anthropic): correct OAuth scope to Max plan + extra usage credits only (#17404)

The previous docs pass (#17399) overstated what Anthropic OAuth works
with. In practice Hermes can only route against a Claude Max plan that
has purchased extra usage credits — the base Max allowance is not
consumed, and Claude Pro is not supported at all. Without Max + extra
credits, users must fall back to an ANTHROPIC_API_KEY (pay-per-token).

Updates the four pages touched in #17399:
- integrations/providers.md
- user-guide/features/credential-pools.md
- reference/environment-variables.md
- getting-started/quickstart.md

website/docs/reference/environment-variables.md

@@ -89,7 +89,7 @@ All variables go in `~/.hermes/.env`. You can also set them with `hermes config
 
 ## Provider Auth (OAuth)
 
-For native Anthropic auth, Hermes prefers Claude Code's own credential files when they exist because those credentials can refresh automatically. OAuth-authenticated Anthropic requests draw from the **extra Claude Code usage included with your Claude Pro or Max subscription** — no separate API key or per-token billing. Environment variables such as `ANTHROPIC_TOKEN` remain useful as manual overrides, but they are no longer the preferred path for Claude Pro/Max login.
+For native Anthropic auth, Hermes prefers Claude Code's own credential files when they exist because those credentials can refresh automatically. **OAuth against Anthropic requires a Claude Max plan with purchased extra usage credits** — Hermes routes as Claude Code, which only draws from the Max plan's extra/overage credits, not the base Max allowance, and does not work on Claude Pro. Without Max + extra credits, use an API key instead. Environment variables such as `ANTHROPIC_TOKEN` remain useful as manual overrides, but they are no longer the preferred path for Claude Max login.
 
 | Variable | Description |
 |----------|-------------|