I read the title and came in ready to agree, but after reading the content of your post I'm a little confused.
There's absolutely an indication of spells you have left. It's right above your action bar. The little boxes. I think that works perfectly well.
Upcasting also makes perfect sense with the UI. You have the base spell icon, then to upcast it, you use the icon that has the "II" on it for 2nd level.
That said, I think the tooltips definitely need work (off the top of my mind, I don't recall any difference in the tooltip for 1st and 2nd level Grease)
I also think the current implementation is bound to get a little crazy in the later levels. You're already looking at a bunch of icons just at level 4, and you're just going to get even more icons later on (both having more variety of spells, and also different spell levels for upcasting). Would rather just 1 icon per spell, and just a different way to choose how to fit it into a higher spell slot.