docs(auth): document fine-grained PAT permission for org publishing (+ pagination-cap test) (#1435)

Follow-up to #1383, surfaced while validating that change end-to-end
against staging.

## Why

#1383 hardened org-namespace publishing to require Owner (`admin`) role,
read via `GET /user/memberships/orgs`. Validating on staging revealed a
gap: the docs only mention the classic `read:org` scope, but a
**fine-grained PAT** (GitHub's recommended token type) needs a
*different* permission to expose org membership. Without it, GitHub
returns no org memberships for the token, so the exchange silently
grants only the personal namespace — with no hint why org publishing
"doesn't work."

This is **not** a code bug (the behavior is fail-closed and correct
given GitHub's response); it's a documentation/UX gap.

## What

- **Docs** (`authentication.mdx`, `github-actions.mdx`): spell out both
token types —
  - Classic PAT → `read:org` scope
- Fine-grained PAT → **Organization permissions → Members → Read-only**
(the equivalent), noting a fine-grained PAT is bound to a single
resource owner.
  - Also clarified `read:user` is not required.
- **Test** (`github_at_test.go`): cover the `maxOrgMembershipPages`
pagination cap — when every page is full, the exchange **fails closed**
(no token) rather than returning a possibly-truncated org grant. This
path was previously untested.
- **Comment** (`github_at.go`): qualify the `X-GitHub-SSO` 403 check as
best-effort — we have not confirmed the memberships *list* endpoint
emits that header on SSO enforcement (it may just omit the org). The
check is safe either way, but the comment no longer overstates it as a
guarantee.

## Verification (live, against staging)

Confirmed by exchanging real tokens for `rdimitrov` on
`staging.registry.modelcontextprotocol.io`:

- **Classic `read:org` PAT** across 16 real org memberships → the JWT
granted exactly the 8 **admin** orgs + personal namespace, and **zero**
of the 8 **member** orgs (incl. `stacklok`, `modelcontextprotocol`) —
the core #1383 behavior, working.
- **Fine-grained PAT**: without Members:read → personal namespace only
(fail-closed); after adding Members:read → the org (Owner) namespace is
granted. This is what the new docs describe.

No runtime behavior change here beyond the added test; the docs and
comment are the substance.

---------

Co-authored-by: Claude Opus 4.8 <noreply@anthropic.com>

docs/modelcontextprotocol-io/authentication.mdx

@@ -53,7 +53,12 @@ GitHub authentication always grants your personal namespace, `io.github.<your-us
 
 To publish under an **organization** namespace (`io.github.<orgname>/*`), you must be an **Owner** of that organization. Ordinary org membership is no longer sufficient: the registry checks your membership role and only grants the org namespace to admins. This prevents anyone who merely belongs to an org from publishing — or overwriting — servers under the org's name.
 
-If you authenticate with a Personal Access Token (for example in CI), the token must include the `read:org` scope for the registry to see your organization role. A token without `read:org` can still publish to your personal namespace, but org publishing will be silently unavailable. The token needs **no** repository scopes — the registry never reads or writes your code.
+If you authenticate with a Personal Access Token (for example in CI), the token must let the registry read your organization role. A token that can't will still publish to your personal namespace, but org publishing will be silently unavailable. The exact requirement depends on the token type:
+
+- **Classic PAT**: grant the `read:org` scope.
+- **Fine-grained PAT**: grant the **Organization permissions → Members → Read-only** permission (the fine-grained equivalent of `read:org`). Without it, GitHub returns no organization membership for the token and you'll get your personal namespace only. Note that a fine-grained PAT is bound to a single resource owner, so it can only see the organization it was created for.
+
+Either way the token needs **no** repository scopes — the registry never reads or writes your code.
 
 ## DNS Authentication