Is it possible to be of sound mind while being an adult virgin, or just a guy who doesn't get laid of have any intimate or sexual encounters with women ever?

Probably not possible to stay sane or grounded without any of the things you mentioned.

Lack of sexual fulfillment absolutely destroyed my mental health in my 20's. It's a critically important aspect of your life to take care of.

I'm trying to make up for it now in my mid 30's. Even if I succeed it won't be the same as it would of been 10 years ago but I've accepted that I had difficult circumstances at that time and it just is what it is.

Do everything you can to take care of it now. Take extreme measures. Push yourself outside of your comfort zone on a regular basis. Don't quit.

I'd recommend goodlookingloser articles to get educated. The dude who wrote those is the most underrated legend of our era.