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This doesn’t mean that they are unsociable or always keep everything secret. They just love to do things by themselves to feel as if they don’t need anyone else doing this for them. Is there any word or phrase that can interpret this full meaning?

Self-sufficient has the connotations of not needing others.

Especially in the second meaning from Dictionary:

having extreme confidence in one's own resources, powers, etc.

He was
self-sufficient, and always reminded you of it.

The word independent comes to mind. It has the positive connotation of being solitary without malice.

Selected meanings from Merriam Webster:

1. 
   

   not dependent: such as
   
   a. (1) not subject to control by others : SELF-GOVERNING
   

   
   
   

   b. (2) not looking to others for one's opinions or for guidance in conduct
   

   
   
   

   c. (1) not requiring or relying on others (as for care or livelihood):
   independent of her parents
   

   
   
   

   d. showing a desire for freedom:
   an independent manner

   
   

It was said:

to feel as if they don’t need anyone else doing this for them

The word autonomous conveys a subtle meaning of rebelling against other people's influence or making a particular statement about being self-sufficient:

[Merriam-Webster]
1 a : having the right or power of self-government

// an autonomous territory
1 b : undertaken or carried on without outside control : SELF-CONTAINED

// an autonomous school system
2 a : existing or capable of existing independently

// an autonomous zooid
2 b : responding, reacting, or developing independently of the whole

// an autonomous growth

Although autonomous is often synonymous with independent, it is not quite as neutral a word; it conveys more of an intention of deliberately breaking away and proving yourself. (The first sense implies it is a right, not just a description of a state of affairs.)

According to the Collins dictionary, a lone wolf is:

someone who is independent and likes doing things on their own, rather than doing them with other people.

"Lone wolf" is also more narrow and unambiguous in its meaning than similar phrases like "independent", which has 22 different definitions on Dictionary.com. Generally "lone wolf" is only used to describe a person or a literal lone wolf.

The Columbia Journalism Review has a really nice article on the origin of the phrase and its connotations through history. For instance:

Not unexpectedly, Native Americans had some legendary chiefs or warriors named “Lone Wolf,” though, as members of tribal communities, they were not really “lone wolves.” (Paraphrased from Ben Zimmer's The Wall Street Journal article)

This example highlights how even the "lone wolves" mentioned weren't complete hermits, either. Rather, they were people renowned for their competence in acting alone while still integrating with their respective communities.

Self-actualizing or perhaps self-reliant are compounds which might serve. Most words for this are negative, so you might have to soften.

Slightly-reclusive.
A bit of a hermit. That sort of thing.

Loner comes to mind.

loner noun

lon·​er | ˈlō-nər

1 : one that avoids others: such as

• a : a person who is often alone or likes to be alone : someone who usually avoids the company of others

From the Merriam Webster dictionary:

He is a moody loner who doesn't become chummy with anyone.

— Sam Moses Many

rowers will agree that sculling is a sport for loners who relish the more quixotic elements of the sport.

— D. C. Churbuck

… she found that the image of the scientist as an antisocial loner is a myth …

— Warren E. Leary

It does often have a slight antisocial connotation, but isn't derogatory at all. Mainly, a loner just likes to do things by themselves.