I have a monolithic application. It is MVC, PHP, all on one server. It does get copied to another server or replicated. There are also older web pages that connect to databases that aren't related to the MVC app at all, adding to the complexity.
I don't have a large team. I don't need big teams from various sections of a business to produce a microservice. But, I do have a lot of databases I have to query and bring back that information into a single web page, transparent to the user. Not just tables, whole databases.
On my application, the back-end, I have IIS, for example, and the application has various models that get the information from the databases. Over time, these models get bloated, or the controller does. Refactoring has to happen (this is my experience anyway.)
This system is older, and new things need to be added, lots of things. It is enough to justify a new web application.
Other than a possible mess, what kind of architecture am I explaining? I want to use REST because other than myself using the API, others can as well. I can simply return JSON to them (and my application).