First, when talking about databases in the Firebase suite, I’m only going to talk about Firestore, and not RTDB (Realtime Database, which was traditionally known as just Firebase). Firebase now refers to an entire suite of services, which includes Firestore, RTDB, file storage, authentication, etc. RTDB is most likely going to be phased out and Google is clearly putting their effort behind Firestore.
Second, there is no manual sharding in Firestore, like there was in RTDB. Sharding is handled automatically by Firestore, so ignore the other answers about that.
Third, you, the customer, own the data in your Firestore database, not Google, so ignore the other answers about that also. If Google, and not the customer, owned that data, Firebase would have virtually no users. And, also contrary to the other answers, you can export data from Firestore. If customers weren’t allowed to export their data, who would ever use it?
Fourth, the suggestion to use SQL technology on your own physical servers (ones that you physically own) is not something that I think belongs in an answer to this question. SQL vs NoSQL and cloud vs in-house are decisions that you should have already made if you’re asking about a specific serverless provider. Clearly (at least apparently), you’ve decided on serverless NoSQL, which is definitely the most popular choice today. And between the two most popular providers, AWS and Firebase, they are designed to handle virtually any workload you throw at it. The most highly-trafficked applications in the world run on NoSQL serverless, like the Amazon marketplace, for example (AWS, obviously). If AWS can handle it, Firebase can handle it too. Google would never design its NoSQL serverless to max out at a certain number of users or level of traffic; it’s designed to scale virtually infinitely.
The only caveat to Firestore (and NoSQL serverless in general, really) is dollar cost—right now in 2019, anyway. Firestore was considerably more expensive only a year ago than it is today, think about that. I think NoSQL serverless will undoubtedly continue to become cheaper, including Firestore. But, right now, with a relatively large userbase, NoSQL serverless, like Firestore, can get expensive. But so can doing it all in-house. An in-house solution still comes with bandwidth cost, in addition to hardware and human cost. Hiring qualified backend engineers to build and maintain an in-house setup is not cheap (hundreds of thousands of dollars a year). Firestore (and DynamoDB) have excellent price calculators to help you predict your costs and you may be surprised to see how cheap it is with a modestly-sized userbase, even with 100k users.