Remove extension code from core header files to prevent core bloating and improve compilation times

[lbushi25]

Is your feature request related to a problem? Please describe

This PR implements the ext_oneapi_forward_progress extension: #13389.
This issue concerns the changes made by this PR to the handler.hpp file. This is a core header file and its ideal to keep it as lightweight as possible for faster compilation times. As a general rule of thumb, by blindly adding extension code to these kind of core headers, the codebase will be bloated and compilation times will suffer with each new extension.

Describe the solution you would like

Refactor the changes made by this PR with the goal of keeping as little code as possible in handler.hpp.

Describe alternatives you have considered

No response

Additional context

No response

[lbushi25]

@aelovikov-intel FYI