Correct string is: Libs: -lpython3.8 then the "/usr/lib/x86_64-linux-gnu/pkgconfig/python-3.8.pc" file becomes:
# See: man pkg-config
prefix=/usr
exec_prefix=${prefix}
includedir=${prefix}/include
Name: Python
Description: Build a C extension for Python
Requires:
Version: 3.8
Libs.private: -lcrypt -lpthread -ldl -lutil -lm
Libs: -lpython3.8
Cflags: -I${includedir}/python3.8 -I${includedir}/x86_64-linux-gnu/python3.8
