This mod adds tabs to the player inventory for nearby chests and other storages.
Mod spotlight

If I understand correctly to add compatibility - "A "simple block tab" is a tab that is opened via interaction with a block. If your block falls under this category, adding a tab is as easy as passing your block to TabProviderRegistry#registerSimpleBlock." - https://github.com/cakewhip/inventorytabs#simple-block-tabs