Apply custom headers in RCTInspectorDevServerHelper (#55609)

Summary:
Pull Request resolved: #55609

Inject custom devsupport headers into the open-debugger POST request. This ensures the debugger launch request includes any registered custom headers.

Changelog:
[Internal] [Changed] -

Reviewed By: cipolleschi

Differential Revision: D93596719

fbshipit-source-id: d4ed0a67b586b8b4e6bbd1817b7cfdf0bd75065f

Author: cortinico

packages/react-native/React/DevSupport/RCTInspectorDevServerHelper.mm

@@ -14,6 +14,7 @@
 
 #import <React/RCTCxxInspectorPackagerConnection.h>
 #import <React/RCTDefines.h>
+#import <React/RCTDevSupportHttpHeaders.h>
 
 #import <CommonCrypto/CommonCrypto.h>
 #import <jsinspector-modern/InspectorFlags.h>
@@ -154,6 +155,7 @@ + (void)openDebugger:(NSURL *)bundleURL withErrorMessage:(NSString *)errorMessag
                                                                escapedInspectorDeviceId]];
   NSMutableURLRequest *request = [NSMutableURLRequest requestWithURL:url];
   [request setHTTPMethod:@"POST"];
+  [[RCTDevSupportHttpHeaders sharedInstance] applyHeadersToRequest:request];
 
   [[[NSURLSession sharedSession]
       dataTaskWithRequest:request