How can two views, both on the same page, both use the same query filter with same URL parameter?
Yes, it is possible to pass same URL parameter to both views, and take effect on both of them, you can disable AJAX search, for example:
Edit both post views:
1) in section "Custom Search Settings", enable option: Full page refresh when visitors click on the search button,
2) In section "Search and Pagination", add a submit button
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