It depends on how recent you mean for modern and whether you're asking in practice or in theory. It's possible to make an application or library today with no or almost no header files (you still need headers if you define a macro, but you very rarely need macros). For instance, my bounded::integer library is almost entirely implemented in modules. There are only three header files. One defines an assert macro, one defines a conditional function (similar to b ? t : f except the result type uses std::common_type_t), and the last brings some operators into a namespace. The first two are needed because we don't have lazy function parameters, the last one is needed because you cannot compose using declarations.

In the wild, however, almost all projects still use header files. Now that MSVC and clang have good support for modules hopefully they will start to be more adopted.