This will likely be one that only shows up on the HUD right after your Inventory changes for a few seconds, but will stay invisible most of the time, because there would be way too many Bars on the HUD if it wasn’t for some of them turning invisible when unneeded.
The Inventory will basically have that Bar visible at all times, with an actual X / Y text imposed on the Bar.
It would be an actual physical Item you start with unless you disable it. Though it would be a Key Item, so it will not drop by itself when you die and actually stay in your Inventory when you respawn. Though “a” Bag will drop containing said Inventory, but the Bag itself will vanish when picked up.
And yep, small Inventories can be a nice challenge. 