I am trying to figure out how much time can it take to develop a sample web app that loads maps in GeoJSON format from the server and draws them in the browser with JavaScript.
I have no experience of working with GeoJSON or drawing geospatial data with JavaScript and my idea is that the starting point to develop the app can be a JavaScript component that draws GeoJSON as demonstrated here, where my GeoJSON looks like this.
If you use a tool like HERE XYZ Studio you upload GeoJSON data to style it, edit data in tabular form, etc. and can get the embed code to publish it in your web app.
There are a few tutorials, in particular the one that shows you step-by-step "Mapping Seismic Activity" from publicly available GeoJSON might be a good start. The other tutorials show you how to do it with Leaflet or Tangram if you wanted to try building your own visualization with a different rendering library.