Problems with CPython on MacOS and Apple M1 chip

Question

I recently moved my content to a new Apple M1 laptop running macOS Monterey and I have some problems with a very simple piece of code that tries to call a Python function from C++. A concrete example is available here.

I installed a new version of Python 3.9.10 via Homebrew, but it seems it is not being detected by my compiler since I get the following errors:

surrutiaquir$ g++ -o main_ctp_fN_grid ctp_fN_grid.cpp -lgsl -lm -lgslcblas -std=c++11
Undefined symbols for architecture arm64:
  "_PyDict_GetItemString", referenced from:
      _main in ctp_fN_grid-2fc2a2.o
  "_PyImport_Import", referenced from:
      _main in ctp_fN_grid-2fc2a2.o
  "_PyImport_ImportModule", referenced from:
      _main in ctp_fN_grid-2fc2a2.o
  "_PyList_Append", referenced from:
      _main in ctp_fN_grid-2fc2a2.o
  "_PyModule_GetDict", referenced from:
      _main in ctp_fN_grid-2fc2a2.o
  "_PyObject_CallObject", referenced from:
      _main in ctp_fN_grid-2fc2a2.o
  "_PyObject_GetAttrString", referenced from:
      _main in ctp_fN_grid-2fc2a2.o
  "_PyString_FromString", referenced from:
      _main in ctp_fN_grid-2fc2a2.o
  "_Py_Finalize", referenced from:
      _main in ctp_fN_grid-2fc2a2.o
  "_Py_Initialize", referenced from:
      _main in ctp_fN_grid-2fc2a2.o
ld: symbol(s) not found for architecture arm64
clang: error: linker command failed with exit code 1 (use -v to see invocation)

I'm really confused about this issue, so any guidance would be highly appreciated. Thanks!