Should I chill out about Mapnik not showing these as buildings, because other renderers might? (Sometimes there’s an unhappy hole in a terrace of buildings just where a particularly significant building sits.) Or should I go and add building=* tags to help them show up?
That’s because they are not tagged as building. Amenity may or may not be building (it might be for example room or the whole area incorporating buildings), so these things are separate.
By the way: “Mapnik” is a name of a rendering engine we (and many other styles) use, the name of default style on OSM.org is OpenStreetMap Carto (or shorter - OSM Carto).
As an example, here’s a nearby amenity=pub where the amenity area includes the fenced-off garden at the back as well as the building: https://www.openstreetmap.org/way/435215642 .
Yes, please add it. It’s typical problem that people add place of worship tag without building for example, while this can be also area other than building (it’s not implied).
Just remember to add it only where you’re sure it’s a building, however it’s mostly easily visible from the aerial imagery. I don’t know what do you mean by bulk editing.
There are a few ways of doing it. As has already been mentioned each one needs to be checked individually so there needs to be a manual review of each one in turn.
One way is to start with taginfo and overpass. I’d normally just start with searching for the tag https://taginfo.openstreetmap.org/tags/amenity=pub and then click the “overpass turbo” link. Then search in the map for Higham Ferrers and comment out the “node” part of the query since that does not apply, and then “run”. The resultant query is https://overpass-turbo.eu/s/EW4 . For each one, right-click the way and open in a new browser tab, and then edit in the browser. On the first one, https://www.openstreetmap.org/way/455420185 , you can see (once you’ve aligned the imagery) that it pretty much matches a building, so it makes sense to add a “building=yes” tag.
Another option is to use the JOSM editor - in there you can do Overpass queries directly, and there’s also a “ToDo” plugin that allows you to work through a list of things to change.
On the wider scale (not really appropriate just to pubs in Higham Ferrers) there’s MapRoulette https://wiki.openstreetmap.org/wiki/MapRoulette , which is designed to automate these sorts of “review a particular issue” tasks.