I know your mod don't support anything other than Baubles, Vanilla-Inventory Slots on transfer dimensions.

Thats why this is just a feature request. We have The-Aether (lecgacy) installed and it seems these slots can be transferred over dimensions as well. The-Aether uses its own slots, similar to Baubles.

I can't tell how it is with the new Aether mod, but The-Aether (legacy aka v1.5.2) has its own Slots, they can be accessed by clicking on the cloud under the character in inventory.

Well thats all so far from me, else keep up the great work!

Could also do the same with betweenlands equipables but idk how that would work, betweenlands doesn't use a typical equip UI for them.

Since you have to get the items from the slots, these slots need to be added to the switch world event. When you have the slots it works with any mod which can put stuff in there (see baubles - they just have baubles as compatibility but it works with thaumcraft/botania items too.)