Each package consists of two modules. The first module is the character, and all the items attached to the character, while the second module has all the common elements, like backgrounds, background items, companions, tokens, effects.
In Season #1, only the second module is shared between the packages using the same Theme, meaning you'll see all available Fantasy backgrounds and companions when editing a Fantasy character, and the same goes for Modern ones. Once you unlock an additional package in Season #1, you'll get new backgrounds and items usable for all Season #1 characters.
In Season #2, every pack in the same base (Female, Male and Muscular Male) can be activated at the same time, and all items are shared between the characters. You can visit the Settings screen to select which packs should be active. Concerning the second module, all backgrounds, items, and companions are automatically active in the given Theme, similar to how it works in Season #1.
In Season #3, since all packages are independent of each other, nothing is shared.