Error including “private” header with CMake

In my library I have seperated the public headers from the source by putting them into include and src. While using Cmake I have this for my library :

target_include_directories(${PROJECT_NAME}
    PRIVATE 
        "${CMAKE_CURRENT_SOURCE_DIR}/include/Thoth"
        "${CMAKE_CURRENT_SOURCE_DIR}/src"
    INTERFACE 
        "${CMAKE_CURRENT_SOURCE_DIR}/include"
)

The idea behind this is that I want the end-user (using the library) to only have the include directory so that they must include like so :

#include <Thoth/file.h>

But within the library I can omit the Thoth.
Now I've also including the src directory within the library because there are some private headers that live there.
This worked alright and I could include every file with the intended path.

When compiling an exe that used the library the library would compile successfully but it would fail on the exe itself.

This was due to the header found within the libraries src not being found. Now that file is not being included in the exe as it is private. But it came from the fact that the exe included a header that had the private header included.

I've played around with some of the settings of visibility and done my googling but I have not found the answer.
How do others deal with separating private and public headers.

Of course I could always use a relative path within the library but I'd rather avoid this seeing as :

#include "../src/private.h"

Is ugly.
Of course if that is the only way, so be it. Though I'd think others would have run into this and wanted a solution.

The other way I could think of is to just include the src folder publicly and trust the user to not include the private header but that would pollute the include path and is undesirably.