I would do it in the same way. Having the nodes for the dumpsters plus the fence and the gate provides all the information required: There is an area where these containers are located. The containers then carry the information it they are used for waste disposal or recycling, if they are located on the ground or underground etc.
Giving the area additional tags makes things quite complicated. This small areas do not qualify for a separate landuse tag imo, I’d say it would rather be another amenity like amenity=dumpster_enclosure but that would not fit the situation in the second pic. And again it would not add any value to the information already provided by the tags given to the different containers plus the fenced area (if there is one).
What I can see there is a paved area where people can walk, if they carry any garbage for disposal or not. The only garbage-related objects are the 5 dumping hoods which can be mapped as nodes with all the necessary details. Tagging this area with landuse=waste or the like would not make any sense imo.