Difficult to help you without looking at your website, I am afraid.
What I can tell you, in any form, you have an action parameter.
This is generally the returning page being displayed, when you do a query.
If your resulting page looks like https://myawesomewebsite.com/?s=test
where ‘test’ is the param you entered, using the GET method this is the default behaviour for any website based on WordPress.
HivePress passes some extra parameters, such as post_type=hp_vendor, hp_listing, hp_request, depending on the page you are on, to niche down your search to such or such entity.
So you may have to pass this extra param, as hidden field for instance.
Your Elementor may even add some complexity to it, by triggering the search results in Ajax.
Let me know if you have solved this issue. Also, please note that we currently don’t 100% support Elementor - while you can add HivePress blocks via Elementor, advanced features are not available yet. I highly recommend using the core WordPress block editor to keep the website fast and lightweight.