How should continental sea shelves be mapped?

There is a natural=continental_shelf listed on the wiki but the tag hasn't been used on anything. The tag sounds reasonable so I would go with that, but don't expect it to rendered anywhere.

Mykhailo, please do not upload data before you know what you are doing. Eventually, before you consult your local community or other forums. Otherwise you may cause harmful effects to OSM.

Just recently you have uploaded a huge multipolygon as this https://osm.org/go/x9WVP--?relation=7160849. There are many critical issues related to this edit: the multipolygon has no qualifier tag (what it is), it is overlap/replica of a fragment of the Global Ocean (defined by the coastline), has different hole structure compared to islands in the coastline, added (illogical) names to coastline segments... just to mention some.

Because osm2pgsql ignores broken/incorrect multipolygons, luckily you have just added a large redundancy to OSM. Obviously, JOSM misses control functions for this kind of edits. If you add to this multipolygon a basic feature tag then you will really cause troubles for most of the OSM map-makers. The best what you could do is to remove the edit, or at least change it to some legal format.

To the shelf sea upload dilemma you already have got a hint. Especially take care of not using feature tags that will conflict with the coastline defined water/land areas. You may see the problem with the "protected area" edits there, simply you cannot clearly see the coastline anymore (it is covered by another area rendering style).