I don't see facet filters and favorites as "client-side state": to me it's "application state", changed by a user interaction. And you're right, it's related to how the state is stored.
As you anticipated, favorites are stored in a database on server-side, so that makes "show me my favorite items" or "show me items related to my favorite articles" the exact same feature as selecting an option in a facet filter.
The state of "I have selected options 1 and 2 in this facet filter, and option B in that other filter" is simply stored in... the URL. And this is why I think it's "application state" rather than "client-side state", and this is why the hypermedia is great IMO: this whole search+facets+favorites+sorting feature becomes nothing more than a <form> with hidden inputs, generating GET requests which URLs are put in the browser history (keywords search, selected options from facet filters and sorting are put into querystring parameters). And that's great, because it happens that one of our features is to send our users custom e-mails with deep links to this the UI, with facet filters pre-selected. All we have to do is generate links with querystring parameters pre-configured, and the user directly gets to a screen with pre-selected facet options, sorting, etc. To me, such behavior cannot be called "client-side state management".
As you anticipated, favorites are stored in a database on server-side, so that makes "show me my favorite items" or "show me items related to my favorite articles" the exact same feature as selecting an option in a facet filter.
The state of "I have selected options 1 and 2 in this facet filter, and option B in that other filter" is simply stored in... the URL. And this is why I think it's "application state" rather than "client-side state", and this is why the hypermedia is great IMO: this whole search+facets+favorites+sorting feature becomes nothing more than a <form> with hidden inputs, generating GET requests which URLs are put in the browser history (keywords search, selected options from facet filters and sorting are put into querystring parameters). And that's great, because it happens that one of our features is to send our users custom e-mails with deep links to this the UI, with facet filters pre-selected. All we have to do is generate links with querystring parameters pre-configured, and the user directly gets to a screen with pre-selected facet options, sorting, etc. To me, such behavior cannot be called "client-side state management".