Thanks for updating this.

Listed building mapping in England has tended to use the following recently:
heritage:operator=Historic England
ref:GB:nhle=*
inscription_date=*
listed_status=*

The older HE_ref=* key is still very common and there may be instances of ref:GB:he.

I don't think I've seen any instances of heritage:ref=* or heritage:since=* before now and taginfo suggests they are very rare in GB, possibly because they're not documented in the wiki.

https://wiki.openstreetmap.org/wiki/Key:heritage#England