Open "Screen Recording" preferences on macOS Catalina

openScreenRecordingPreferences.m

static void sOpenScreenRecordingPreferences()
{
    CFDataRef  passThruData = CFBridgingRetain([@"Privacy_ScreenCapture" dataUsingEncoding:NSUTF8StringEncoding]);
    CFArrayRef itemURLs     = CFBridgingRetain(@[ [NSURL fileURLWithPath:@"/System/Library/PreferencePanes/Security.prefPane"] ]);

    OSStatus  err = noErr;

    AEDesc    passThruDesc = {0};
    BOOL      needsDispose = NO;
    
    if ((err == noErr) && passThruData) {
        err = AECreateDesc('ptru', CFDataGetBytePtr(passThruData), CFDataGetLength(passThruData), &passThruDesc);
        needsDispose = (err == noErr);
    }
    
    if (err == noErr) {
        LSLaunchURLSpec launchSpec = { NULL, itemURLs, &passThruDesc, kLSLaunchDontAddToRecents|kLSLaunchAsync , NULL };
        LSOpenFromURLSpec(&launchSpec, NULL);
    }

    if (needsDispose) AEDisposeDesc(&passThruDesc);
    if (passThruData) CFRelease(passThruData);
    if (itemURLs)     CFRelease(itemURLs);
}

Even easier, use a URL of: x-apple.systempreferences:com.apple.preference.security?Privacy_ScreenCapture

From Terminal:

open "x-apple.systempreferences:com.apple.preference.security?Privacy_ScreenCapture"