Hi Phoebe,
The issue is the combination of that custom query and the plugin. The regular elementor Posts shortcode does not have that. It must be pushing a custom query/override query, which the search cannot recognize and use.
I think, that the only possible solution is, to add the same inclusion rule to the search as well, you can read about taxonomy term based inclusions here. That way, the results will be restricted to the same tag, that should do it.
Please note, that I cannot guarantee that this combination is going to work, as that is not the native elementor posts widget, but a custom one.