If you are using Elementor Pro, you need to use our extension for it, which can be installed after clicking the big blue button (you need to be logged in to see it) at the top of the guide page (to download the installation file):
https://searchandfilter.com/documentation/3rd-party/elementor/
Note towards the end of that guide, which shows how you can set the form to WooCommerce Shop.
Make sure that Product Category is in the form (even if you use CSS to hide it), and …
1. Set autodetect category/taxonomy:
https://www.screencast.com/t/3B40jPYRF4SA
2. And also set ‘Enable filtering on Taxonomy Archives’:
https://www.screencast.com/t/piCPyshb6
Then you can use the same form on all category pages.