I know it wasn’t an (or the) OSM site, and by context no one including me said it was. That exists at https://www.openstreetmap.org/. It was a site that took advantage of the OSM data. Any semi-intelligent person who can read and understand English would be able to discern that https://garmin.openstreetmap.nl/ was not OSM by reading the header. But, not everyone is good with reading, I guess. That it caused problems for “people” strikes me that it was their problem. It never professed to offer any kind of tech or map support, just aggregated cards of selected areas using the most up to date data at the time the map was requested.

Regardless, the BBBike site fulfills the same function, and the site I linked above is spot on for the OP’s needs in that it has an already aggregated set of maps for Europe, if the OP would like to skip the steps required for using BBBike (which aren’t onerous, but do require some attention to detail).