Did you know that you can use SharePoint search query language to bring back audience targeted content?
So, you’ve implemented Audience Targeting in your Modern SharePoint Libraries.
As a recap, you can do this by going to Library Settings -> Audience targeting settings:

And then check the box to “Enable audience targeting”:

Now you’ve enabled audience targeting, you can use SharePoint search query language to bring back audience targeted content.
For example, a search for all published news pages can be accomplished with the following KQL query:
PromotedState:2
To augment this to include only audience targeted new pages, try this:
(PromotedState:2 AND ModernAudienceAadObjectIds:{User.Audiences})
And to also include pages that are not targeted at all:
(PromotedState:2 AND (ModernAudienceAadObjectIds:{User.Audiences} OR NOT IsAudienceTargeted:true))
You can use this trick from search boxes:

And of course you can also use it from custom code (including projects like the excellent Modern Search Web Part on GitHub).
The Highlighted Content Web Part has this functionality built in:

Happy audience targeting!