I've been looking all over the web for a solution to a client problem. They refuse to retire their 16-bit dbase database, but still want us to development real-time PWA web applications to read/write to the dbase system.
If it is even possible to get a RESTful API server working with 16-bit dBase?
Yes. You can create a PWA app with dBase or any DB, which has option to communicate to modern programming languages via APIs like JDBC, ODBC. Then that programming language of your choice, say JAVA talking to dBase via JDBC, can expose the functionality via RESTFul service.
For a PWA app, underlying back-end service tech stack is masked over plain HTTP requests. So it doesn't matter what back-end service you use and what DB that talks to in turn, for a PWA
As an update on your “real time “ need, not sure what kind of real-time functionality you are planning and on expecting what ETA/SLA. While no doubt you can build a PWA with any dB as stated above, it can certainly impact its performance. If you need something like googles auto suggest which pulls up results as you type, you need something like “in-memory” DB.
So the question is more of what performance your DB can support and what is expected. I do not see any feasibility challenge with respect to PWA.