Guerilla added an option to disable pickup animations.It's kinda slow because your character stops while the action is being performed. It would be nicer if it was Forged Odyssey or TLOU style where the animation targets the pickup but your legs keep working.
Heads Up: You can now Disable Pickup Animations in the Settings : horizon
Which is kind of fascinating to me.
Also I couldn't find any limits in the inventory. I have over 200 rocks in my pocket lol.