Do INTERFACE FILE_SETs not propagate along target dependencies?

Usage
1

I have a header-only library:

add_library( "Lib" INTERFACE )

target_sources( "Lib"
    INTERFACE 
        FILE_SET myHeader 
            TYPE HEADERS
            FILES "${CMAKE_CURRENT_SOURCE_DIR}/myHeader.h"
)

and an executable that depends on it:

add_executable( "App" "main.cpp" )
target_link_libraries( "App" PRIVATE "Lib" )

My hope was that since myHeader was an INTERFACE FILE_SET that I could find it (or its files) in the executable’s target properties, similar to how e.g. an include directory from the interface target would be found in the executable’s include directories.

I tried using $<TARGET_PROPERTY:HEADER_SET_myHeader> and $<TARGET_PROPERTY:HEADER_SET> on the executable target, but both were empty …

Am I missing something or do INTERFACE FILE_SETs not propagate along target dependencies?

(I used a header file to simplify things in the example; my actual use case involves shader files that I’d like to propagate from libraries that own them to the executable that compiles them. And while I can achieve that with custom transitive properties, I was hoping FILE_SETs would provide a more elegant solution.)