Someone from another forum found a solution to this issue, so I am going to post his answer here so that others will have any easier time finding it.
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Since you're on Chernarus Winter, I tested it alongside CUP Units/Vehicles for custom loadouts. I had the same trouble you had so I opened a Bohemia official Zeus scenario in the editor to see what they were doing and it was actually really simple.
In the F5 category in the editor, there is 2 modules that are both called Game Master and you need both. The first is F5 > Gameplay Modes > Game Master. The second is F5 > Zeus > Game Master.
Synchronize the Zeus module (edit the attributes to allow unofficial addons to access mod loadouts) to the Gameplay Modes module.
From there, spawn your regular Zeus curator system module and make sure its variable name is the same as the "owner" listed in the Zeus Game Master module.
When you launch the scenario as Zeus, you will have to place the respawn point for the respective player teams before you can continue, but when you open the Respawns > Loadouts module you should see a tab for each team as well as all your custom loadouts in dropdown menus.
Credit to u/manthedanville on Reddit.