Embarcadero still ships Delphi. That is not the problem. The problem is a Delphi 5 or Delphi 7 application written twenty years ago by someone who has since left, on components that no longer compile, with the only person under sixty who can read Object Pascal already booked. Job postings for Delphi maintainers stay open for a year.
I learned Delphi in the 1990s in my father's shop and never stopped. I built a manufacturing execution product in it that is still sold twenty-five years later, and I have spent fourteen years building modern .NET on top of a Delphi/InterBase back office that the client rightly refused to throw away. Sometimes the right architecture is to keep the Delphi and put a modern front end on it. Sometimes it is a staged move to C#. I can read the code well enough to tell you which.
Silverlight has no runtime left. The exit is screen by screen, not a rewrite.
LightSwitch generated your app. The tooling to regenerate it is gone.
Your records are in Notes databases. Getting them out is the job.