Good news. The Istanbul-Sofia route has officially resumed running on April 25th (yesterday)!
You can find the timetable here > https://www.bdz.bg/en/c/international-rail
The ALternative is quite easy: BUS. (or fly, of course, but then its better to fly from West-EUR and not shorter distance in the region).
The rails/trains were/are burocratic state-institutions, neglected for many years and demand fell so much that hardly anyone used them. Plus all the new made borders in what once was 1 country; Yugoslavija also did not stimulate travel. As for now a few major lines are being renovated and thats why there are no train at all-untill maybe a better future.
Exactly same Q has been posted here by now a few dozen times-just scroll down and read more.
Site seat61.com has in /en/ an overview of all current overland routes+Alternatives from UK to all EUR countries. Or change plans -EUR has still some 25+ other countries in the pass-scheme with much better links!
To Serbia there are currently only two daily international trains:
Bar/Podgorica (Montenegro) - Belgrade
Kelebia (Hungary) - Subotica
It is possible that in a few months the train Ljubljana - Zagreb - Belgrade does return.
If you count Kosovo as a part from Serbia, there is one daily train between Pristina and Skopje
There currently no trains between Europe and Turkey :/
In May, the Optima Express will make the route Villach - Edirne (not included in the Railpass)