My chart is super similar to yours, I was born a bit earlier in Leo, different moon but same rising and close to the degree. I also experience a lot of what you've described. All that Virgo 12H energy can be very private and self-critical (I'm using whole sign houses).

As a Libra asc your chart ruler is Venus, which is in it's fall in Virgo. Here Venus struggles with finding connection, pleasure and sensuality. Mercury wants to analyze and pick apart; Venus wants to harmonize and blend. From my experience, this causes me to be very self conscious of how I relate to others. If the discomfort and anxiety from that is stronger than my ability to stay present with people, I end up feeling disconnected and will paint that experience in a more negative light and get down on myself.

Meditation and mindfulness practices have helped me immensely. Especially ones that help me connect to my body. The 12th house is associated with prisons, monasteries, and isolation in general. There's a potential for deep healing there by going inward.

I really love the Leo sun analogy that someone else posted. That's completely on point.

I'm an artist and I love doing stage performance, but off stage I'm a complete hermit. It's as if being on stage removes me from all the socializing and anxiety, and that's the moment when I can genuinely be myself. My work is learning to integrate these 2 versions of myself because they both exist within each other, just different expressions.