Fix stepper SSR/hydration flash: server reads cookie, cache bypass

Three changes to eliminate the stepper flash:

1. home-stepper.sx: server path reads cookie via (get-cookie) for
   step-idx initial value. Client path reads document.cookie via
   def-store. Both default to 0 when no cookie exists.

2. sx_server.ml: bypass response cache when sx-home-stepper cookie
   is present. Render on main thread (not worker) so get-cookie
   sees the parsed request cookies.

3. site-full.spec.js: flash detection test sets cookie=7 via
   Playwright context, checks SSR HTML matches hydrated state.

Test: "No flash: SSR=7 hydrated=7 (cookie=7)" — passes.
Tested on fresh stack=site server subprocess.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

hosts/ocaml/bin/sx_server.ml

@@ -3040,8 +3040,10 @@ let http_mode port =
           in
           write_response fd response; true
         end else if is_sx then begin
+          let has_state_cookie = Hashtbl.mem _request_cookies "sx-home-stepper" in
           let cache_key = if is_ajax then "ajax:" ^ path else path in
-          match Hashtbl.find_opt response_cache cache_key with
+          match (if has_state_cookie then None
+                 else Hashtbl.find_opt response_cache cache_key) with
           | Some cached -> write_response fd cached; true
           | None ->
             if is_ajax then begin
@@ -3062,6 +3064,18 @@ let http_mode port =
                       (escape_sx_string (Printexc.to_string e)))
               in
               write_response fd response; true
+            end else if has_state_cookie then begin
+              (* State cookie present — render on main thread so get-cookie works.
+                 Don't cache: response varies by cookie value. *)
+              let response =
+                try match http_render_page env path [] with
+                  | Some body -> http_response body
+                  | None -> http_response ~status:404 "<h1>Not Found</h1>"
+                with e ->
+                  Printf.eprintf "[render] Cookie render error for %s: %s\n%!" path (Printexc.to_string e);
+                  http_response ~status:500 "<h1>Error</h1>"
+              in
+              write_response fd response; true
             end else begin
               (* Full page: queue to render worker *)
               Mutex.lock render_mutex;