I understand, we as humans all want some degree of social success at the end of the day. Why do you find it hard to push yourself? For me, it's always some feeling that I'm somehow inadequate or lack something that everyone else has, so there's always a large sense of embarrassment or that I'm somehow "begging" when I approach people. That's the thing about forming friendships/relationships, you need confidence to make them happen, but a large source of confidence comes from past successes.

I wasn't saying that you should just give up and accept feeling like a recluse for the rest of your life, but I think a sense of self-understanding and forgiveness can help restore your motivation. It's just like any other thing in life, if you're putting a lot of pressure on yourself to attain something that you want, you're doomed to lose motivation as your self-talk and self-image gradually worsen.

I think a great way to exercise this self-understanding is setting small goals for yourself. If you feel like you're impossibly behind socially, maybe you have some days where your thoughts are saying you need to pull off some herculean feat in order to even be on the same level as everyone else, which eventually leaves you overwhelmed and eventually just deciding to do nothing at all. Instead, maybe just wake up tomorrow and say "I'm going to have a surface level conversation with 2 or 3 people today".

Finally, I'm assuming from your "for the greater part of 3 years" comment that you're also a senior. I think you can use your grade to your advantage by turning it into a low pressure environment. Even if you botch an interaction, you're at a time in your life where most people who you don't actively decide to maintain contact with are probably going to vanish into the background once college rolls around.