Fix failure calling json function over cxxbridge (#25898)

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",
 ]