docs(apps): make the workspace functions URL the primary route-serving story (#22693)

Part 5 of the app-docs audit series (after #22688–#22691).

## The problem

`front-components.mdx` warns that the legacy `/s/` route is deprecated
and **deactivates on 2026-07-24** (16 days from now), but the rest of
the docs still teach `/s/` as the only serving path:
`logic-functions.mdx` ("Exposes your function ... under the `/s/`
endpoint"), `logic/overview.mdx` ("A request hits your `/s/<path>`
endpoint"), and the document-generator tutorial fetches
`${TWENTY_API_URL}/s/...` from front-component code. A developer
following those pages today ships an app that breaks on Cloud in two
weeks.

## What this changes

- **logic/logic-functions.mdx** — httpRoute triggers are described as
served at the workspace's functions base URL (what the server injects as
`TWENTY_FUNCTIONS_URL`; a dedicated per-workspace domain on Cloud, per
`WorkspaceDomainsService.buildPublicFunctionBaseUrl`), with a warning
box covering the `/s/` deprecation and the self-host fallback.
- **logic/overview.mdx** — trigger table no longer hardcodes
`/s/<path>`.
- **document-generator tutorial** — the `curl
http://localhost:2020/s/...` examples stay (they're correct against the
local dev image, where no isolated functions domain exists), with a note
explaining the Cloud behavior. The front-component code snippets now use
the `TWENTY_FUNCTIONS_URL || TWENTY_API_URL + '/s'` fallback pattern —
the same one Twenty's own published apps use (e.g.
`packages/twenty-apps/public/call-recorder`).

Only English sources were touched; `l/<locale>` copies come from
Crowdin.

---
_Generated by [Claude
Code](https://claude.ai/code/session_01ExboyDAT19khDuKXaYXETT)_

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---------

Co-authored-by: Martin <martin@twenty.com>

packages/twenty-docs/developers/extend/apps/tutorials/document-generator/building-the-ui.mdx

@@ -91,9 +91,11 @@ const GenerateDocumentForm = () => {
   }, []);
 
   const generate = async () => {
-    const apiBaseUrl = process.env.TWENTY_API_URL;
+    // Prefer the injected functions URL; fall back to the legacy /s prefix (self-hosted/local)
+    const functionsBaseUrl =
+      process.env.TWENTY_FUNCTIONS_URL || `${process.env.TWENTY_API_URL}/s`;
     const token = process.env.TWENTY_APP_ACCESS_TOKEN ?? process.env.TWENTY_API_KEY;
-    const res = await fetch(`${apiBaseUrl}/s/documents/generate`, {
+    const res = await fetch(`${functionsBaseUrl}/documents/generate`, {
       method: 'POST',
       headers: { 'Content-Type': 'application/json', Authorization: `Bearer ${token}` },
       body: JSON.stringify({ templateId, recordId }),
@@ -186,7 +188,9 @@ const DocumentViewer = () => {
   const recordId = useFrontComponentExecutionContext((c) => c.recordId ?? null);
   // ...load { content, file } for recordId, then derive the links:
   const pdfUrl = document.file?.[0]?.url;
-  const webUrl = `${process.env.TWENTY_API_URL ?? ''}/s/documents/view?id=${recordId}`;
+  const functionsBaseUrl =
+    process.env.TWENTY_FUNCTIONS_URL || `${process.env.TWENTY_API_URL ?? ''}/s`;
+  const webUrl = `${functionsBaseUrl}/documents/view?id=${recordId}`;
 
   // Render the template body, plus quick links to the web page and the PDF.
   // Links open in a new tab so they don't navigate the embedded component.

packages/twenty-docs/developers/extend/apps/tutorials/document-generator/http-routes.mdx

@@ -9,8 +9,15 @@ The same handler can also answer HTTP requests. We'll add two routes:
 - a **POST** endpoint the UI calls to generate a document, and
 - a public **GET** endpoint that renders a document as a printable web page.
 
-Both use `httpRouteTriggerSettings`. App routes are served under `/s` on your
-Twenty server (e.g. `http://localhost:2020/s/documents/generate`).
+Both use `httpRouteTriggerSettings`. On the local dev server, app routes are
+served under the `/s` prefix (e.g. `http://localhost:2020/s/documents/generate`).
+
+<Note>
+On Twenty Cloud, routes are served on the workspace's dedicated functions domain
+— the URL Twenty injects as `TWENTY_FUNCTIONS_URL`, with no `/s` prefix. The `/s`
+prefix is deprecated there and only remains for self-hosted and local instances.
+See [Calling a logic function](/developers/extend/apps/layout/front-components#calling-a-logic-function).
+</Note>
 
 ## POST route — generate on demand