“but it is indisputable that different countries use different criteria to register covid-deaths”
In regard to death certification most countries use the WHO recommendations in the International Statistical Classification of Diseases and Related Health Problems (ICD). Most have similar death certificate design.
Co-morbidities are present in nearly all deaths whether from covid or anything else. You need to be careful your prevalence of co-morbidities doesn’t just represent the prevalence of said co-morbidities in the general population.