docs: move implementation sections out of the handbook pages

Three handbook pages carried sections an operator never reads, named after
source paths and build internals. They move to pages under 4-implementation,
and each handbook page keeps a short pointer.

- forge.md: the notification poller (what it polls, how it formats,
  de-duplicates and marks notifications read) is now
  agent-tools/forge-notify.md. The forge page keeps a short Notifications
  section.
- matrix.md: the retired hive-side matrix code, the evaluation assertions and
  the fluffychat-web build fixes are now networking/matrix-homeserver.md.
- github.md: the Implementation section (how `gh` and `git push`
  authenticate, and the GitHub poller) is now agent-tools/github.md.

docs/README.md and the agent-tools README list the new pages, and AGENTS.md's
note on mixed operator and implementation docs now says to move the detail
and leave a pointer.

docs/README.md

@@ -99,9 +99,9 @@ Accounts outside the swarm that an agent can hold. Start at
 [`2-handbook/external-accounts/`](2-handbook/external-accounts/README.md).
 
 - **How to give an agent a GitHub account (`gh` + `git push`)? how's
-  the PAT injected?** → [`2-handbook/external-accounts/github.md`](2-handbook/external-accounts/github.md)
-  (operator content up top; the `gh`/git-push + notification-poller
-  mechanics are in a collapsed "Implementation" section at the bottom).
+  the PAT injected?** → [`2-handbook/external-accounts/github.md`](2-handbook/external-accounts/github.md);
+  the `gh`/git-push and notification-poller mechanics are in
+  [`4-implementation/agent-tools/github.md`](4-implementation/agent-tools/github.md).
 - **How to give an agent GitLab accounts (`glab` + `git push`, more than one
   instance)?** → [`2-handbook/external-accounts/gitlab.md`](2-handbook/external-accounts/gitlab.md).
 
@@ -119,6 +119,11 @@ Nothing of it sits in this tree.
 - **What can an agent do inside its container? bash, subagent, forge, matrix, and the
   `hive-forge`, `swarm-logs` and `swarm-metrics` CLI references?** →
   [`4-implementation/agent-tools/`](4-implementation/agent-tools/README.md).
+- **How does the forge notification poller wake an agent, and how does it
+  format and de-duplicate what it delivers?** →
+  [`4-implementation/agent-tools/forge-notify.md`](4-implementation/agent-tools/forge-notify.md).
+- **How do an agent's `gh` and `git push` authenticate to GitHub?** →
+  [`4-implementation/agent-tools/github.md`](4-implementation/agent-tools/github.md).
 
 ### Turn loop, scheduler, CI, observability
 
@@ -141,6 +146,9 @@ Nothing of it sits in this tree.
   discovery work?** → [`4-implementation/networking/gateway.md`](4-implementation/networking/gateway.md).
 - **How does DNS resolution work in agent containers? What's the
   bridge network for?** → [`4-implementation/networking/network.md`](4-implementation/networking/network.md).
+- **What does the matrix homeserver's module assert at evaluation, how
+  fluffychat-web gets built, and what replaced the hive-side matrix code?** →
+  [`4-implementation/networking/matrix-homeserver.md`](4-implementation/networking/matrix-homeserver.md).
 - **Where do agent snapshots go? How does the swarm's `btrfs receive`
   endpoint authenticate a pushing hive?** →
   [`4-implementation/networking/snapshot-store.md`](4-implementation/networking/snapshot-store.md).