Similar to ZBXNEXT-7512, I would like to propose, to add just another item into the context menu. If you compare the current side-menu with the context menu, you might notice a difference:

So, besides the inconsistencies in both lists, I propose to add "Monitoring ⇾ Host" to the menu.

In the meantime, this can be circumvented, by making use of the new custom context menu URLs from ZBXNEXT-3496:

By adding the following "Script", you can build something like I requested: