There is no centralized ID number, the closest is your social security number but this is basically only outbound for PAYE tax and haphazardly correlated to your pension payments in late life.
Everything operates on a “trust system” where you often present paper (!) with whatever address you claim to be living at as proof you are real (e.g. opening bank accounts).
Passport loss is rectified by seeking out “professionals” with government-approved occupations that are not related to you that can vouch you are actually the person you are trying to replace a passport for.
The entire thing is a mess and living in digital-identity-native Europe is a dream come true that you should be extremely thankful for.