Introverts don’t get lonely if they don’t socialize with a lot of people, but we do get lonely if we don’t have intimate interactions on a regular basis.
I really hate being an introvert because I sometimes think “oh hey, I can totally hang out with a bunch of people right now! I can handle it! I hate being alone!!” and then three hours into hanging out I realize how draining of energy it is for me to be around other people and I just want to curl up into a ball and isolate myself for the rest of my life.
Sometimes those who don’t socialize much aren’t actually anti-social, they just have no tolerance for drama and fake people.
Never chase anyone. A person who appreciates you will walk with you.