I have accumulated quite a few healing items, and advice I have found elsewhere suggests that some, at least, can be used in battle. However, the inventory option in battle shows only my scanner (and nets when I had them).

The potions specifically say they cannot be used in battle, so I understand why they don't appear.

Attempting to use the draughts and elixirs from my normal inventory in another tab fails too, because I am not allowed to use my inventory in battle.

How do I use my healing items?

The healing systems in the lower-level areas are a bit wonky. It gets easier in the lv50+ areas, I think (the adventure/battle format gets updated).

To use elixirs/draughts in battle, you actually have to click the red swooshy arrow /next/ to the inventory satchel button on the battle page. Then click "use item", select the one you want to use, and click on the pet who needs it. Go on with your fighting turn as normal, and the item will be used during that round.