Filter results from search instance

Hi,

I face the following problem: I have configured the search to redirect to this custom url “/xxxxxxxx/?s={phrase}&post_type=product” (“xxxxxx” is my woocommerce product permalink base). I have also selected the option “Οverride the default WordPress search results with results from this search instance”

When I do a search, indeed I get redirected to woocommerce and everything seems fine. But when I use the left bar filters, the filtering does not happen for results from the search instance. Instead the default wordpress search results are being filtered.

Example:

Searching for “example” leads to this url:

https://cosmorama-travel.gr/xxxxxx/?s=example&asp_active=1&p_asid=3&p_asp_data=1&current_page_id=-10&woo_currency=EUR&qtranslate_lang=0&filters_changed=0&filters_initial=1&asp_gen%5B%5D=title&asp_gen%5B%5D=content&asp_gen%5B%5D=excerpt&customset%5B%5D=product

Then when I select a category the search {phrase} gets lost:

https://cosmorama-travel.gr/κατηγορίες/κατηγορία-ταξιδιού/ατομικά-ταξίδια/?s=example

If you would like to see it for yourself, you can use this link:

https://cosmorama-travel.gr/ταξίδια/?s=ελλάδα&asp_active=1&p_asid=3&p_asp_data=1&current_page_id=-10&woo_currency=EUR&qtranslate_lang=0&filters_changed=0&filters_initial=1&asp_gen%5B%5D=title&asp_gen%5B%5D=content&asp_gen%5B%5D=excerpt&customset%5B%5D=product

Is there a way to prevent the search {phrase} from being replaced/ignored?

Kind regards,
George