However, e.g. whitehouse.gov refers to "President Clinton" in its description (for the act of being born, not for his active role as president).

https://www.whitehouse.gov/1600/presidents/williamjclinton

Where I live, Finland, a "President" is the official title for former presidents (there are now three alive) so I should actually address them as such. The current one is formally referred to as "President of the Republic". I can't really check how this is with Russia.

I'm not convinced. Multiple other sources say you retain the title for life and also recommend addressing the person as such. Obviously it's a matter of etiquette and not right or wrong, though.