In the cms, if i go to admin > content type, I am able to add properties to existing page/block types.
In the scenario a content editor wants to do this, how do these newly added properties get rendered on the page if they're not part of the razor template?
They will not be rendered on the page. There is many metadata properties like sortorder, publish dates etc that typically dont get rendered. You can however in code like in a controller have logic that is based on the value of such metadata properties.
In the modern versions of Episerver 7+ all properties should be added via code, they should never be added in the admin backend. The feature still exists as a legacy area, mainly the type view is uses to delete properties that have been removed from code and to check the settings. Adding properties should only ever be done by a developer, in code.
CC, please read more about how to do this by code here:https://world.episerver.com/documentation/developer-guides/CMS/Content/
Also install the Visual Studio extension found here:
Then create a demosite (Create new project and include Alloy through the episerver menu item) and look how it is done there
So, it sounds like before Episerver 7 there was a way to do this, and in current version this is no longer supported.
Is this correct?
Yes. Back then we used PageTypeBuilder to get properties etc to get synchronized with code (so that we didn't need to do that by hand which is/was error prone).
As Scott already said, you shouldn't be using admin to modify these but have them in code (you get your changes to different environments automatically when you deploy code, that is the way to do it).