Then it's a programmer error, since the actual Hunger of Hadar isn't actually a summon but a conjured gateway to the cold of space.
Based on how the handbook reads at least, the bitter cold is the bitter cold of space region being opened and the acid damage is from the "otherworldly tentacles rubbing against".
Basically if it doesn't spawn an actual creature for the purpose of being controlled by the player / AI, it shouldn't be treated as a summon. Trying to separate the two skill parts would also create an overly complicated coding problem.
This would also mean that while its being treated as a "conjured creature" it receives zero benefit of items that affect either the players spells OR the players summons, as its not really a true summon. Making a very blanket bland spell functionality that interacts with zero items as a result.
TLDR: Should just work as a normal spell with the two damage parts under the hood. Treating it as a "conjured creature" that deals damage overcomplicates it and ruins the fun video game synergy that finding items in game to use alongside it gives.