(1) An apt adjective is self-contained which means quietly confident and self-sufficient, comfortably alone in a positive sense.
1.(of a thing) complete, or having all that is needed, in itself.
"every section of the painting is a self-contained unit"
synonyms: complete, independent, separate, free-standing, enclosed
2. (of a person) quiet and independent; not depending on or influenced by others.
"he's very self-contained"
(2) a good concept for your personal use: Aloneness is a word specifically used to mean 'alone' in a positive sense. Even if defined negatively as a synonym of solitude or loneliness in some standard dictionaries, it is used self-affirmingly as a contrast to loneliness which has negative connotations.
My sister who is an expert psychologist and ace in spirituality has suggested this word (which I had never heard of till now!) AND confirmed the positive connotation and usage of 'aloneness' as a positive attitude to being alone.
Example of usage: Loneliness vs. Aloneness: What’s the Difference?
By Pragito Dove at Huffpost blog (These are not definitions but contrasting interpretations by the author.)
Loneliness is a lack, a feeling that something is missing, a pain, a depression, a need, an incompleteness, an absence.
Aloneness is presence, fullness, aliveness, joy of being, overflowing love. You are complete. Nobody is needed, you are enough.
My sister (who is herself an extrovert, but spiritual) asked me in relation to this question, "why should being alone be perceived as being lonely? When I am alone I am with myself."
I suspect that spiritually advanced people have reclaimed and redefined the word 'aloneness' specially to counter the negative connotations acquired by 'loneliness' because of the herd mentality that 'man is / must be a social animal.' However this word is not yet widely used and may only convey the meaning of loneliness if you use it to describe yourself to others, unless you are willing to explain its positive connotations.
See this article for the full text of the above extract: