I did a quick test and it is indeed possible to upload a file using guest user in a community. Below are further details on your specific questions.
Is it possible to upload files as a guest user in a community?
Or does this checkbox/setting only work with the aura component file:upload?
The Org setting is applicable for LWC as well.
Could I ...
I don't think you can do it due to the external sharing restrictions on the object for the site guest user. Even if you manage to find some workaround using without sharing in apex etc., be mindful of the new security updates coming up for the guest user documented here. That means that as of March 2020 the user will be even more locked down and limited to ...
The actions appears on Object home page comes through List View option in search layout for the object.
The step would be:- Setup--> Object Manager--> Select the Object --> Click on Search Layout for Classic--> You will see below options:-
Click on the drop down option against the List view and select edit. You will see below:-
You can identify weather ...