I am not convinced to expose security/config keys to client. I would not call it secure, not because some one can steal all private information from first day, because someone can make excessive request, and drain your quota and make you owe to Google a lot of money.
You need to think about many concepts from restricting people not to access where they are not supposed to be, DOS attacks etc.
I would more prefer the client first will hit to your web server, there you put what ever first hand firewall, captcha , cloudflare, custom security in between the client and server, or between server and firebase and you are good to go. At least you can first stop suspect activity before it reaches to firebase. You will have much more flexibility.
I only see one good usage scenario for using client based config for internal usages. For example, you have internal domain, and you are pretty sure outsiders cannot access there, so you can setup environment like browser -> firebase type.