Cutting off connections with social world eventually leads to lack of confidence and social skills.
I'm not advocating for introverts 'cutting off connections' as you put it. Social interaction is important for health, especially in your developmental years, and obviously a lack of social interactions will lead to a lack of social skills.
In my experience as an extremely introverted person and someone who has wanted to become more extroverted, forcing myself to go to social gatherings and "be extroverted" was a huge drain on my emotions and energy. Even a regular environment like going to school leaves me wanting to stay in my room for a couple hours to unwind. From what I understand, extroverts feel the opposite, and will organize outings with friends to energize themselves.
I truly do wish I had spent more time developing social skills and less time reading in my early years, especially elementary school, but it wouldn't have made me more extroverted.
I myself became an introvert and was really happy with my life but
still social life with friends, teachers and relatives was missing.
You don't 'become' an introvert just like that. It's a spectrum, and even relatively extroverted people can adapt to low social environments, but they won't thrive inn the same way.
To answer the original post, an introvert in their ideal environment (low/optional social stress, limited interactions outside of their friend/family, and time to themselves) is just as happy as an extrovert in their ideal environment (high interaction volume/intensity, new experiences, parties, etc.)