Have you checked the WordPress Template Hierarchy Diagram To get an idea how wordpress choose the tempalte. I’m not sure but according to the WordPress Template Hierarchy, WordPress will choose default archive.php for custom taxonomy if no special template is specified.
That means you cannot not have archive-product.php to use with Custom Taxonomy archive.
In your case the – example.com/product/?price=100 is archive for prodcts with custom taxonomy price set to 100.
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