docs: restructure into topic subdirectories, collapse duplicated index

Per mara's go-ahead on hyperhive#3902 ("getting started is good, but
terminal rendering does not go in there i think"):

Moved 21 top-level docs/*.md files into 7 new topic subdirectories
(existing web-ui/, turn-loop/, swarm/, tools/, crates/ untouched):
  getting-started/  setup.md
  agent-lifecycle/  agent-hierarchy.md, approvals.md, persistence.md
  trust-boundary/   boundary.md, security.md
  integrations/     forge.md, matrix.md, github.md, knowledge.md
  networking/       gateway.md, network.md, snapshot-store.md
  scheduler/        jobq.md, coordinator.md, ci.md, observability.md
  process/          conventions.md, gotchas.md, pr-review-gate.md
  web-ui/           terminal-rendering.md (moved into the EXISTING dir,
                    per mara's correction to the original getting-started
                    guess -- it's UI implementation detail, not onboarding)

The physical layout now matches docs/README.md's own topical headers,
which already amounted to this taxonomy -- see the scoping comment on
the issue for the two findings that motivated this (a genuine
duplication between CLAUDE.md's old "Reading paths" list and
docs/README.md's grouped one, since drifted out of sync with each
other; and the flat layout not matching the grouping we already had).

Fixed every cross-reference this moved across the whole repo (~120
files: docs/ internal links at every depth, Rust doc comments, nix
module option docs, crate READMEs) -- verified two ways: a grep sweep
confirming zero remaining references to any old path, and a script
that resolves every markdown link in docs/**/*.md + CLAUDE.md +
README.md against the filesystem and reports anything that doesn't
exist (zero broken links).

Collapsed CLAUDE.md's "Reading paths" section (the duplicate) down to
a pointer at docs/README.md, now the single index. Rewrote
docs/README.md itself to use the new subdirectory paths and added the
one doc it was missing that CLAUDE.md's old copy had (pr-review-gate.md).

Classified all 22 docs/*.md files first via a haiku subagent (mara's
suggestion) on two axes -- proposed grouping and operator-vs-
implementation focus -- before finalizing the taxonomy; spot-checked
the report and found internal inconsistencies (its classification
table disagreed with its own summary section for a few files), so this
taxonomy is my original proposal + the one correction mara gave
directly, not a blind application of the subagent's table. The
operator-focus data it gathered is still useful for a follow-up
content pass (docs skewing 'mixed' rather than pure operator-facing),
not addressed in this PR -- structure only.

nix fmt clean, both pre-push lints clean.

docs/tools/matrix.md

@@ -130,7 +130,7 @@ pending invites, resolve_invite to accept or reject`. The keyed todo
 is cleared when a `resolve_invite` (or `join_room`) call resolves the
 invite.
 
-See [`docs/matrix.md`](../matrix.md) for the homeserver setup,
+See [`docs/integrations/matrix.md`](../integrations/matrix.md) for the homeserver setup,
 provisioning flow, and federation config.
 
 ## Extra MCP servers (per-agent)