When giving yourself an Item Frame using this command:

  "/minecraft:give @s item_frame{EntityTag:{Invisible:1}}"

And then spam clicking that item on top of a regular Item Frame in your inventory eventually the NBT disappears and the items stack. Also, sometimes weird client desync happens, where they stack and unstack, but eventually the NBT is actually gone from the item. This has been tested to happen in Creative and Survival mode.

Additionally, when getting an ItemStack with the invisible:1 EntityTag from InventoryClickEvent#getCursor the mentioned NBT tag never appears in the gotten ItemStack. The same thing happens when trying to get the ItemStack from the players hand while they hold the special NBT Item Frame using this:

ItemStack hand = p.getInventory().getItemInMainHand();

The returned ItemStack does not have the NBT tag