Show on a diffrent dmg bar if there a free slots - so the player sees if new item types can be added to the backpack or not.
Maybe display like EnderIO Empowered tools/armor with a second dmg bar in a different color.

atm I have no other elegant idea if something pop up in my head I write here

Alright, let's break this down a little.

Currently, the damage bar shows one bar, that represents how full the pack is overall. It shows in terms of absolute fullness without regards to slots and respects maximum stack sizes in each slot.

Is what you would like to see just the number of slots that are empty? That could just be represented as another number above the existing bar. Or I could introduce an advanced damage bar upgrade that shows 2 damage bars (as you suggested): the first showing the absolute fullness (general indicator) and the second showing the number of slots filled.

Alright, after writing it out I think I'll do the latter; a new advanced variant dmg bar upgrade that shows 2 bars: 1 for overall fullness and 1 for slots filled. Thanks for the suggestion!

A second bar requires a coremod

Ah does it? I was going to look into how EnderIO/EnderCore does it, but if it's that nasty I likely won't bother. I'll figure out some other solution then.

Yeah they use a coremod :p

Hmm, well then maybe I'll add a way to toggle the damage bar between showing overall fullness and slots used. That might work, although I don't think it will be quite as ideal. @Hancho2009, thoughts, would that be fine?

I think It is usefull to see at a glance how full the bag is and at the same time if there are free slots for new Item types. I think a toggle will not cut it. sry :-(
What about color coding the dmg bar. For example green: has free slots and red: no more free slots?
Or maybe an other boolean type indicator?

thanks for looking into this

I just looked into colors for the damage bar, unfortunately not possible in 1.10 (it's easily done in 1.11) without a bunch of hackery. It was a good idea, but unfortunately not feasible. If you have other suggestions I'd love to hear 'em.

Improve Damage Bar Upgrade With Colors To Show Open Slots

As it's easy to do the colors in 1.11+, I'll just implement this for the 1.12 rewrite.