I wanted to find out if there is ability to save customers interests. Customer should have ability to choose some favorite categories from the list of all categories. Based on this "favorite categories" the categories should be displayed on home page. Is there any application or something what allows to save that in customers account?
For "favorites" that's often just wishlist apps; though I don't know any that specifically allow collections/entire-products-in-collections to be marked.
If that doesn't exist you will probably need a theme customization to build the UI to hook up any of the below option to some sort of star/heart button instead of a form input. And then to also render specific collections in specific pages based on what's favorited.
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To not involve third party apps a possible klunky workaround is setting favorites as part of a purchase where you pass the favorites in as cart attributes, or line-item-properties, and then in shopify-flow assign the values to a customer metafield.
Coorect on what @PaulNewton said, there are apps that you can use to collect additional information from the customer and save it in customer metafields.
I think it'd be the easier way to achieve what you need, and for the case you mention, you can create something like a multi-choice field so the customer can tick the categories from a predefined list.
Later you can add liquid or a custom block to the theme to render the customer metafield (if the customer is logged in).
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