When editing Menus, I find 5 typs of items that can be added:
Would it be possible to add custom ones? Let's say for instance that I want to add an image, or a search bar, or whatever.
Could I somehow add new menu items types, that render the code that I choose for them?
Not in the menu management interface.
You can inject custom elements if you create a custom nav walker. This requires some coding skill as well as trial and error to figure out which parts of the code you need to use, and how to tweak them.
Or, if you're comfortable using JavaScript to change things after the menu is built (so some visitors and search engines might not see the change), you could use a document.ready script that identifies a "regular" menu item and then injects whatever image etc. you want to display in its place.
You will need a plugin for that. For example, something like this one: https://wordpress.org/plugins/wp-megamenu/
