But there is no option to appear in the filter menu and not on the favorites?

If you meant have particular custom filter to the default filter list, you need to modify view

let's assume you want to have a custom filter for "Sale Price" over 10

first, you need to find the field name. activate the developer mode (i.e. help, about, activate developer mode)

edit a product

move the mouse over "Sale Price" and you will find the field name: "list_price"

Also, you would find that the object is "product.template"

then go to the setting, section (top bar) and select Technical->User Interface->Views

there search for views based on their object. i.e. put product.template in the search box and select the second item in the search box which searches over "objects"
then you will find that from "search" views, "product.template.search" would be the main view and others have been inherited from that

open it

and add this:

                    <filter string="over10" name="over_10" domain="[('list_price','>=',10)]"/>

save, go to any product search page (as you have modified the main search view) and you will see "over10" in the list of predefined filters

Add filter in the search view and set context "search_default"+"name of filter" to 1.

Eg:

<filter string="Active" domain="[('account_type','=','normal')]" name="name_of_active"/>

Add context in action

<field name="context">{'search_default_name_of_active':1}</field>