Introverts are the most likely to be lonely tbh. It's less that they receive energy by being alone but rather that the "social battery" recharges when alone. It has nothing to do with the need of human interaction.

Wanting to make dinner and being physically hungry are two different sensations. I can absolutely be hungry but not have the energy to make dinner. In the same way, I can be in need of social interaction while still not having the drive to go out and do it.