I have been getting quite a few Pokémon eggs and am currently filled up to my maximum 9/9 capacity. Will purchasing a Pokémon Storage Upgrade increase this amount? I ask because both regular Pokémon and eggs are listed under the Pokémon section of the UI.
Purchasing a Pokémon storage upgrade will not increase your egg capacity beyond the initial nine that are allowed (I have purchased several Pokémon capacity upgrades). Unfortunately there is currently no way to increase your egg capacity, although it is possible this feature will be added in the future.