How to properly tag something that is e.g. both a sculpture, a monument and an archaeological site?

Dear I propose to solve it as follows:

All 6 should be considered as artwork and they belong together as part of the art project "Kunst på Skovlunde Flyveplads", as described on the website. Group all of them together in a cluster or group relation (cluster preferred because used more often, see https://wiki.openstreetmap.org/wiki/Relations/Proposed/Cluster) . Give it as name the name of the project name=Kunst på Skovlunde Flyveplads, and add any additional tags that are common to all. Members of this relation don't need a role. Members can be nodes, ways or areas. All of these members will have tourism=artwork and artwork_type=sculpture on their respective nodes or areas. Don't add these keys to the cluster, as clusters are not intended to group common key features.

This gives you the option to tag the "Monument SAI", drawn as an area with it's primary purpose, namely artwork. Add an additional node in the middle to identify it as a monument. No problem here as it is a single point you can go to. You state it is not an official monument, but I would not bother, as described on the website it is intended as one. In the name of this new node I would describe it as the name also should be unique, suggestion: name=Monument SAI-Skandinavisk Aero Industri A/S memorial. As it refers to an archaeological excavation you could add another new node in the same area and tag it as archaeological site, again with a new name, suggestion: name=Monument SAI-SAI KZ I airplane excavation. I would not add another cluster to this area with it's to new nodes inside. It is obvious they belong together, you just use additional nodes to make it's multi-purpose use clear.

Leaves us with one challenge: "Farm Fiction". It is not referred to on the website as part of the project, so don't include it in the cluster relation. Leave it as is an area tagged as sculpture. You could add a note to it to describe it in some detail.

The site, but correct me if I am wrong, is an old airfield turned into a park/sports centre. It should be considered as a heritage site (see https://wiki.openstreetmap.org/wiki/Key:heritage. So I would make a relation with type=boundary, boundary=protected_area, protection_class=22, key=heritage(see https://wiki.openstreetmap.org/wiki/Tag:boundary%3Dprotected_area#Social-protected-area) and create a boundary around the area. Now you can make the artwork cluster relation, and "Farm Fiction" part of it (and any additional areas as you wish), all get the role=inner. Consider adding a single node to add the name and give it the role=label. Give it a unique name and additional common keys.

So to summarize: all items except the monument will have unique tagging. The Monument SAI will have tagging on the area as a sculpture, it's primary purpose, and additional 2 nodes inside identifying it also as a monument and archaeological site. All sculptures are clustered with the projects in which they were created. The site is marked as a heritage site and all artwork, the monument node and archaeological node are part of it.