Hi Chris
Maybe it's because I'm used to Toolset, but I can't get the "Related" option for the Posts module to display anything meaningful at all (and Elementor haven't updated their documentation yet to describe how it works).
I make a sandbox test site with a very simple set up that you are welcome to look at: hidden link (no login credentials required).
Note, I just have Types and Elementor (incl Pro) plugins.
I made a custom post type "Stuff" and added a custom taxonomy "Locations" to it with a few countries, and I added tags to posts with the same countries.
I made one Elementor template for the locations archive.
You can see it on the front-end here: hidden link
If you edit the template you'll see the first section is the archive, which correctly displays "stuff" posts with the Japan location term.
The second section has a Posts module with "related" setting that I can't get to work. Feel free to edit and update to demonstrate how it should, it would be useful to know.
The third section just takes a Posts module which is set to display standard posts with a tag of "Japan".
I had to set this tag manually, and I guess this is the crux of your question. Can you set the tag dynamically, based on the archive term.
Well, evidently no.
But. In the Query section you can manually set a Query ID to allow server side filtering.
So, much like we provide hooks such as wpv_filter_query to modify Views filters, it seems Elementor provide something similar to modify these queries.
You'll need to try their support for help with that if you can't work it out from their documentation.
Note that I don't have Views active on this test site. And there is nothing I've done with Types that you couldn't do by manually registering the post type and taxonomies, so I think it really is a question for Elementor.
(But do let me know if you have anything useful to share about that related posts widget.)