How relevant is mechanical engineering to marine engineering? Is a professional engineer with marine/submarine background eligible for (marine engineering) work on passenger vessels?

I understand that the certifications are different. Does anyone have experience in this department?

gracias.

This only my opinion
Mechanical engineering has (IMHO) no relevance to Marine engineering.

A professional engineer with experience is not eligible without the correct certs. What you have to do to get your certificates, depends on where and how much experience you have and where you are applying.
Your qualifications must be STCW95.

A couple of Guys I trained with, went on to get there Mech Eng Degree, this allowed them more openings ashore.
But I never heard of anyone going the other way.

Bit like making sow's ear out of a silk purse!