There is a generic tag for items ("BlockEntityTag"). If the item has this tag, it will be applied to the block entity after placement - provided that you haven't overridden onlyOpCanSetNbt or the player is op.
This is what shulker boxes use as well using the copy_nbt loot function. Look at the shulker box loot table to see how it is done.
Basically just the title
My current idea is that I can use the "getDrops" method like in the ShulkerBoxBlock class and apply a "item tag" with the data, but I am not sure if an "item tag" is even a thing nor how to properly use the "getDrops" method (do I retain the loot table for the block).
Is there another mod that does something like this that isn't related to container items like shulker boxes, just some type of data? If so a link to it would be the only help I need. If not, then would someone mind explaining how this might be done?