docs: pilot split of github.md into operator-facing + collapsed implementation

hyperhive#3902, mara: option (a) - a content pass splitting mixed docs
into operator-facing content plus implementation detail. One file
first, to agree on the split pattern before doing the other ~19.

Went through 3 shapes on review before landing here: a sibling
-internals.md file (mara: clutters the navigation), then two
tree-precedent alternatives damocles raised (subdir+README like
web-ui/; or only split docs with a pre-existing boundary marker,
which would've covered 3-4 of the ~20 flagged docs and left the rest
untouched), then mara's own proposal - a collapsed <details> section
in the same file. Verified empirically (cmark-gfm --unsafe, the
website's own render pipeline) that markdown headings nested inside a
<details> block still parse as real headings with heading-id anchors
once separated from <summary> by a blank line, so anchor links into
the collapsed section keep working.

github.md keeps enabling/provisioning/security up top; its
'Implementation' section is now a <details> block holding what was
briefly a separate github-internals.md (deleted again) - how the
agent's gh/git-push actually authenticate, and the notification
poller's internals. Reverted the two cross-references + the
docs/README.md entry back to pointing at github.md now that the
content lives there again.

Added a short CLAUDE.md note recording the pattern per mara's ask,
including the one real caveat damocles flagged: <details> only
collapses in a rendered browser, a raw-text read (cat, the Read tool)
still sees everything, same as today.

CLAUDE.md

@@ -209,3 +209,12 @@ with each other.
   thing is, not to how much investigation it took to find it — a
   mechanical fix gets a one-line comment, a genuinely non-obvious
   invariant or decision earns real prose.
+- **Operator-facing doc with real implementation detail mixed in**: wrap
+  the implementation part in a `<details><summary>…</summary>` block
+  (blank line after `<summary>` so the markdown inside still renders,
+  not a second file) rather than splitting into a sibling page — see
+  `docs/integrations/github.md`'s "Implementation" section. Zero nav
+  churn, works uniformly regardless of whether the doc already had a
+  clean boundary. Caveat: it only collapses in a rendered browser —
+  reading the file as raw text (`cat`, the Read tool) shows everything,
+  same as today.