Apparently, only because of one thing...

See:
https://onlinelibrary.wiley.com/doi/10.1111/jopy.12504

"We found that the correlation between the energy level facet and well‐being was solely responsible for the association between extraversion and well‐being. Neither sociability nor assertiveness were uniquely related to well‐being when energy level was included as a predictor. Thus, the correlations between well‐being and sociability and between well‐being and assertiveness can be almost fully explained by these constructs’ relationships with energy level.Conclusions

We conclude that the link between extraversion and well‐being should be attributed to the energy level facet rather than generalized to the trait level."

So, if they're right, extroverts "feel" better because they have more energy.

Sounds right to me. I taught myself to be much more sociable than is comfortable for me. I've described before how a vacation with my husband's family, all of whom I dearly love and who are such fun to be around, winds up exhausting me. They got used to my taking long walks by myself or going to my room for two hours to read. I need to recharge my batteries every once in a while. :)