Unfortunately there is no current support for this (thanks to the pack we might now though, as they finally have a use), so you will have to manually update every Object Catalog aka swatch.
Go to the Warehouse, click on the first Object Catalog, look for a "Styles" section, it's not very far down so you should see it almost immediately. Click the Edit Items button across from it, the object may or may not already have an entry. If it doesn't click the "Add" button and a section will be added, then once you've found your style of choice fill in the Group, Type, and Instance that matches.
If it does already you only need to replace the Instance with the style you want (or you're lucky and it already matches).
As for the instances in question, open the Game File Cruiser, look for the "Styles" filter option and select it. A whole list will appear with the options you are looking for. Find the one you want and copy the Instance into the field (and Group and Type if you had to manually add it).
And then you repeat for every Object Catalog in the package. This seems to be all you need to do for it to appear in the styled section of the catalog (and another creator confirmed the other day).
I did find some tags, but even EA objects with a Styles entry don't use these, but you're welcome to try manually adding these in the Tag section to see if it helps.
<T ev="2534">Build_StyleBoho</T>
<T ev="2535">Build_StyleContemporary</T>
<T ev="2536">Build_StyleCosmoluxe</T>
<T ev="2537">Build_StyleBasics</T>
<T ev="2538">Build_StylePatio</T>
<T ev="2539">Build_StyleDoubleGallery</T>
<T ev="2540">Build_StyleFrenchCountry</T>
<T ev="2541">Build_StyleGothicFarmhouse</T>
<T ev="2542">Build_StyleMission</T>
<T ev="2543">Build_StyleModern</T>
<T ev="2544">Build_StyleQueenAnne</T>
<T ev="2545">Build_StyleShotgun</T>
<T ev="2546">Build_StyleSuburbanContempo</T>
<T ev="2547">Build_StyleTudor</T>
<T ev="2548">Build_StyleIsland</T>
<T ev="2549">Build_StyleGarden</T>
<T ev="2550">Build_StyleScandinavianContemporary</T>
<T ev="2555">Build_StyleMidCentury</T>
