In your case, you are using a pre-written SDK which knows how to connect to Firestore, does caching and updates application data when needed, and provides a standard method of reading, writing and deleting data in Firestore (with associated documentation and example data from google).
Therefore, using an API (as described for the mongoDB) is not required and is undesirable.
There are some cases where you might want to have no read or write access to a firestore collection or document, and in this case, you could write a cloud function which your app calls with parameters, that receives the data that you want to write and does some sort of checking or manipulation beyond the capabilities of cloud firestore rules (although these can get pretty sophisticated). See https://firebase.google.com/docs/firestore/security/get-started
Todd (in the video contained in this link) does a few good videos on this subject.
However, this is not really working in the same was as the API you mentioned in your question.
So in the case of using Firestore, you should use the SDK and not re-invent the wheel by creating your own API.
If you want to share photos for example, you can also store them in firebase storage and then provide a URL for other devices to access them without your app being installed.
If you want to write something to firestore which is then sent to all other users then you can use listeners on each app, and the data will be sent to the apps after it arrives at Firestore.
https://firebase.google.com/docs/firestore/query-data/listen gives an overview of this.
One thing to always look at with firebase is the cost of doing anything. Cloud functions cost more than doing a read of a firestore document.
This gives an overview of pricing for different capabilities within the firebase set of capabilities.
https://firebase.google.com/pricing