Stages do not work with this mod, however it does work with pretty pipes storage mod. Not sure why/how the hooks work.

Define doesn't work.

Are there errors in the log?
Have you tried staging the container?

Recipes behind the stage, are shown, and create a phantom item, but when you try and craft nothing pops out.
So, this mod has a crafting terminal, and it looks like it implements the normal crafting bench stuff...

https://github.com/tom5454/Toms-Storage/blob/master/src/main/java/com/tom/storagemod/gui/GuiCraftingTerminal.java

However you can't craft staged recipes with it

Not to add on too much, but it's the same behavior with the sophisticated backpacks integrated crafting bag

If you aren't getting any errors, that means that it should support Container staging.
https://docs.blamejared.com/1.16/en/mods/RecipeStages/RecipeStages#packages-and-containers

So I'm confused, if I give a terminal a stage, does that terminal forever act at that stage, or does it's stage now reflect the user of that terminal?

It forever has the stage.

If we don't have a player, we can't possibly know what stage a player has to tell the terminal so it can do things correctly.

Well thanks for the info, I was able to get the terminal to craft that stage. Now the question becomes, why does a normal crafting table work, restricted by player, and one in a mod does not?

If the inventory gives us a player, we can work with it, simple as that, it doesn't even need to be a normal vanilla table, just needs to give us the player.

Although in cases like this, and AE2 / RF auto crafters, you simple don't have a player at all, so the package / container stuff was added so at-least there is some support.