chore: drop dead NEXT_PUBLIC_GATEWAY_URL; refresh Phase P increment status

.env.example: NEXT_PUBLIC_GATEWAY_URL has zero consumers anywhere in
apps/, packages/, or plugins/ — the SPA is origin-relative by design and
the legacy Next tree never reads it. Remove the whole stale Web App
section so new deployments stop configuring a dead variable.

PHASE-P-STRUCTURE.md: increment map was stale — P3 is merged (PR #1151,
repair PR #1154) and P4 is in progress (P4-1 read-only projects + tasks
merged, PR #1153). Re-verify the doc against next head 3bd490c0; add the
P4-1 pages to the tree listing. Blocker #1145 remains open and the P5/P6
rows are unchanged.

webui-audit S1 hygiene items (lane REPORT.md).

.env.example

@@ -40,11 +40,6 @@ BETTER_AUTH_SECRET=change-me-to-a-random-32-char-string
 BETTER_AUTH_URL=http://localhost:14242
 
 
-# ─── Web App (Next.js) ───────────────────────────────────────────────────────
-# Public gateway URL — accessible from the browser, not just the server.
-NEXT_PUBLIC_GATEWAY_URL=http://localhost:14242
-
-
 # ─── OpenTelemetry ───────────────────────────────────────────────────────────
 # OTLP HTTP endpoint (otel-collector or any OpenTelemetry-compatible backend)
 OTEL_EXPORTER_OTLP_ENDPOINT=http://localhost:4318

docs/webui/PHASE-P-STRUCTURE.md

@@ -1,7 +1,7 @@
 # WebUI Phase P — File / Folder Structure & Migration Map
 
-> **Status:** living document — first pass. Structure and increment status are verified against
+> **Status:** living document. Structure and increment status are verified against `next` as of
-> `next` as of merge `8c27024d`. Details (per-surface component inventories, exact route tables,
+> merge `3bd490c0` (2026-08-26). Details (per-surface component inventories, exact route tables,
 > test matrices) are still being fleshed out; extend the stub sections below rather than rewriting
 > the verified structure.
 
@@ -29,7 +29,8 @@ apps/web/
     ├── routes.tsx                 # ── SPA React Router route table
     ├── spa/                       # ── NEW SPA surfaces
     │   ├── guards.tsx             #    guest / authenticated route guards
-    │   ├── pages/                 #    login, register, sso-callback (P2); chat + error boundary (P3)
+    │   ├── pages/                 #    login, register, sso-callback (P2); chat + error boundary (P3);
+    │   │                          #    projects, project-detail, tasks (P4-1)
     │   └── chat/                  #    P3 typed chat: use-chat-connection, commands-panel,
     │                              #    session-panel, message-transcript, tool-call-list, composer
     │
@@ -84,8 +85,8 @@ build path is retired.
 | ------ | ---------------------------------------------------------------------------------------------------------------------------------------------- | ----------------------------- | ------------------------- |
 | **P1** | Vite + React Router skeleton beside Next (entry, router, guards, vitest)                                                                       | `feat/webui-p1-vite-skeleton` | ✅ merged — PR **#1143**  |
 | **P2** | SPA data layer + same-origin auth (login/register/SSO pages, guards, relative api/socket/auth-client)                                          | `feat/webui-p2-data-auth`     | ✅ merged — PR **#1144**  |
-| **P3** | Typed SPA **chat** (`spa/chat/*`, `chat-contract.ts`, chat page + error boundary)                                                              | `feat/webui-p3-chat`          | 🚧 in progress (unmerged) |
+| **P3** | Typed SPA **chat** (`spa/chat/*`, `chat-contract.ts`, chat page + error boundary)                                                              | `feat/webui-p3-chat`          | ✅ merged — PR **#1151** (+ repair PR **#1154**) |
-| **P4** | Port **projects / tasks / settings / admin** dashboard surfaces into the SPA                                                                   | _tbd_                         | ⏳ not started            |
+| **P4** | Port **projects / tasks / settings / admin** dashboard surfaces into the SPA                                                                   | `feat/webui-p4-1`             | 🚧 in progress — P4-1 (read-only projects + tasks) merged, PR **#1153**; settings/admin remain |
 | **P5** | **Cutover**: Gateway serves the Vite `dist` on `:14242`; flip `dev`/`build` to vite; **remove** the legacy Next `app/` tree + `next.config.ts` | _tbd_                         | ⏳ not started            |
 | **P6** | CI / images (trails): build the SPA in CI, ship images                                                                                         | _tbd_                         | ⏳ trails                 |