I have furnaces automated to use lava buckets. So there are basic inventory hoppers inserting lava buckets at the back, normal (vanilla) hoppers inserting items to be smelted at the top, and basic inventory hoppers removing items from the bottom.

When you places items into the furnace to be smelted (either via the vanilla hoppers on top or manually, doesn't matter how) then the smelting operations starts, the lava in the bucket is used, the empty bucket is properly removed from the furnace's fuel slot, and a new full bucket of lava is placed in the fuel slot.

However, smelted items are not removed from the furnace. They just stay in the furnace. If I destroy the basic inventory hopper that is removing items from the bottom of the furnace and replace it with a new basic inventory hopper then items are properly removed, but only until the lava bucket needs to be replaced again. When this happens smelted items quit being removed from the furnace.

Tom's Simple Storage 1.7.0 on Minecraft 1.20.1 using Forge 47.2.0.