Hi hunilazar,
Thanks for reaching to us.
The Search Results template does not exist, because it is a normal archive (of products or posts). Therefore, I recommended you to use WoodMart WooCommerce Layouts builder, which is powerful WoodMart feature, with the condition Search page https://prnt.sc/PQanWcUQpz68
And you can use Result count
widget to display number of results. Some predefined layout already has it and it hidden, you just need to re-enable it https://prnt.sc/hzP_PU14OHm7
Here is the documentation:
https://xtemos.com/docs-topic/woodmart-woocommerce-layout-builder/
Regards,