"Sometimes, when you introduce Prolog in an organization, people will dismiss the language because they have never heard of anyone who uses it. Yet, a third of all airline tickets is handled by systems that run SICStus Prolog. NASA uses SICStus Prolog for a voice-controlled system onboard the International Space Station. Windows NT used an embedded Prolog interpreter for network configuration. New Zealand's dominant stock broking system is written in Prolog and CHR. Prolog is used to reason about business grants in Austria."
Some other notable real projects using Prolog are TerminusDB, the PLWM tiling window manager, GeneXus (which is a kind of a low-code platform that generated software from your requirements before LLMs were a thing), the TextRazor scriptable text-mining API. I think this should give you a good idea of what "Prolog-shaped" problems look like in the real world.
Others have more complete answers, but the value for me of learning Prolog (in college) was being awakened to a refreshingly different way of expressing a program. Instead of saying "do this and this and this", you say "here's what it would mean for the program to be done".
At work, I bridged the gap between task tracking software and mandatory reports (compliance, etc.). Essentially, it handles distributing the effective working hours of workers across projects, according to a varied and very detailed set of constraints (people take time off, leave the company and come back, sick days, different holidays for different remote workers, folks work on multiple stuff at the same time, have gaps in task tracking, etc.).
In the words of a colleague responsible for said reports it 'eliminated the need for 50+ people to fill timesheets, saves 15 min x 50 people x 52 weeks per year'
It has been (and still is) in use for 10+years already. I'd say 90% of the current team members don't even know the team used to have to "punch a clock" or fill timesheets way back.
Any kind of problem involving the construction, search or traversal of graphs of any variety from cyclic semi-directed graphs to trees, linear programming, constraint solving, compilers, databases, formal verification of any kind not just theorem proving, computational theory, data manipulation, and in general anything.
