Thus seems not the place to debate the use of food:* and drink:*.

Perhaps on the forums https://community.openstreetmap.org/t/new-tag-structure-food/99638 or wiki https://wiki.openstreetmap.org/wiki/Key:food:* or https://wiki.openstreetmap.org/wiki/Proposal:Food_declaration?

In either case usage seems fitting with https://wiki.openstreetmap.org/wiki/Key:food:*. And this allows searchability for food/drink products, whereas a menu link does not. How else would an app have data that piroshki is served at From Russia with Love cafe https://openstreetmap.org/way/1428332092.