You can put items in forges via chute, but it doesn't work properly
Whenever you try chuting in fuel or anything else it gets placed like it's being heated (even if it cant). Attempting to add something other than the original item placed in deletes it, which could make for a nice trashcan.
When ever you place items in that can be heated, you can put in a whole stack of that item before it starts deleting it's self (same for any other item). After it's all in the forge, if you fuel it by hand and start it you can heat up an entire stack of bloom or ingots for only one or two pieces of fuel and it goes really fast.
Afterwards the forge becomes a bit too buggy to work properly, so you have to break it. You can pull out individual items mid heating, but cannot put it back in.
I am on 1.22.2 stable and tested this in creative, I have not had the chance to test it in survival.