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

### Is your feature request related to a problem? Please describe

This PR implements the ext_oneapi_forward_progress extension: https://github.com/intel/llvm/pull/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_