It would cost less starting out compared to your own server, you may only have to pay per function call. Whereas you would have to pay for server space from the start even if no one is using your product.
A framework may be overkill if all you want to do is run a function when something in your database changes. Firebase is a good example of this, you can trigger functions when a document changes.
As a developer, I have 2 screens and multiple desktops per screen.
Screen 1: Chrome on desktop 1, VS Code desktop 2.
Screen 2: Database on desktop 3, Postman desktop 4, Slack/Email Desktop 5.