Filtering News posts across sites using tags or categories

This is definitely an advanced skill, but it is not hard to do. I am not aware of any step by step instructions for how to do it but here is a quick way to do a demo to show how it works. You will need to learn about managed metadata, site columns, and the News web part for this to work - as well as options for provisioning sites (which is a completely different topic that you'll want to research). Once you are familiar with these basic terms, here's what you can do. Let's say you want to categorize all news on any site with a News Type. To do that, first create a Term Set in the SharePoint Admin Center for News Types. Make sure each value is unique. Then, create a managed metadata site column on each site called News Type and point the column to the term set you created at the root of your tenant. Add the site column to the Site Pages library on your sites. Now, every site has a column with the exact same name and a shared set of values. You will need to actually create and publish pages with the values for this to work, but once you've got all your content created, you can select the sites you want to roll up in the News Source and then filter using a Managed Property. Find the column you created (it will have a name like owstaxIdNewsType) and use filter options to find Property Name Contains whatever term you are looking to roll up. You have several options for making sure all sites get created with the appropriate columns, but your goal is to ensure that all sites are provisioned with the columns that you need.