The only reasonable design is to have two kinds of API keys that cannot be used interchangeably: public API keys, that cannot be configured to use private APIs, and private API keys, that cannot be configured to use public APIs. There's no one who must use a single API key for both purposes, and almost all cases in which someone does configure an API key like that will be a mistake. It would be even better if the API keys started with a different prefix or had some other easy way to distinguish between the two types so that I can stop getting warnings about my Firebase keys being "public".

It'd be much better to call them something like "API usernames" or "API Client IDs". Though I also dislike the naming of "public keys" in asymmetric cryptography, for the same reasons, and I'm definitely not winning that fight!