Recent versions of QGIS support vector tiles in the MVT format (like these ones). So with a suitable style you should be able to create a layout using vector tiles and print.

Assuming you meet the relevant attribution/license requirements for the various bits you choose of course. I don't think any usage policy has been published for these tiles yet.

Unfortunately there are some translation issues with styles for MVT sources so you might need to do a bit of fixing if you don't want to go the route of a paid plan with MapTiler (third party provider) who have a plugin.

There's also a list of "print map" generators of varying types here: https://wiki.openstreetmap.org/wiki/OSM_on_Paper