What's the right firestore architecture for managing client API keys?

Can someone put me in the right direction? I need a Firestore collection to store user-related API keys.

The simplest Firestore structure I can think of might look like this:

Firestore-root
  |
  --- users (collection)
       |
       --- $uid (document)
            |
            --- apiKeys: ["apiKeyOne", "apiKeyTwo", "apiKeyThree"] //Array
            |
            --- uid: "userId" //String
            |
            --- createdAt: October 21, 2021 at 2:46:19 PM UTC+3 //Timestamp

So sometimes I want to retrieve a list of all API keys that belong to a user.

Assuming that you are using Firebase Authentication, to do that, simply use the following lines of code:

firebase.auth().onAuthStateChanged((user) => {
  if (user) {
    var uidRef = db.collection("users").doc(user.uid);
    //Process the data
  }
});

But oftentimes, the scenario is that my API is getting a request with an API key attached and then I need to quickly validate whether this API key exists.

To solve that, you have to check whether a specific API key already exists using:

var queryByApiKey = db.collection("users").where("apiKeys", "array-contains", "apiKeyToCheck");

Should the API key be the ID?

No, there is no need for that.

And will I be able to efficiently get a list of API keys that have a specific UID too?

Sure, as already explained above.