This might be helpful: https://ggullentops.blogspot.com/2018/07/sitecore-sxa-search-overview-pages.html
Adding the filter to the page is not that hard - it's a standard component. Getting the facet that is used by the filter component right is a bit more tricky.
If you want to have a facet on a single line text you should use a List Facet
. Create your facet in the facets folder "Tenant/Site/Settings/Facets/" and set the Field Name
. This has to be the lowercase name of the index field that is used for the facet (your product type). Check your index to get the correct name...
Next step: go to "Tenant/Site/Data/Search/Checklist Filter" and create a new Checklist filter. Select your facet and adapt texts as needed.
This filter item will be the datasource for the Checklist component that you can put on your page.