Fix failure calling json function over cxxbridge

It is not entirely clear what is the underlying mechanism for this
failure, and it should be investigated further. On Windows Debug builds,
any calls to functions like `json::convert_all_numbers_to_string` were
causing a runtime crash. Bisecting our branch has revealed that this
crash started after an entirely unrelated change [1] that in fact seems
quite anodyne.

This change correct the runtime failure with a minimum change.

Resolves brave/brave-browser#41497

[1] #25830

browser/sources.gni

@@ -139,6 +139,7 @@ brave_chrome_browser_deps = [
   "//brave/components/ai_chat/core/common/buildflags",
   "//brave/components/ai_rewriter/common/buildflags",
   "//brave/components/body_sniffer",
+  "//brave/components/brave_adaptive_captcha",
   "//brave/components/brave_ads/browser",
   "//brave/components/brave_ads/core",
   "//brave/components/brave_component_updater/browser",
@@ -503,7 +504,6 @@ if (is_win && is_official_build) {
 brave_chrome_browser_public_deps = [
   "//brave/app/vector_icons",
   "//brave/browser:browser_process",
-  "//brave/components/brave_adaptive_captcha",
   "//brave/components/brave_sync:constants",
   "//brave/components/variations",
 ]