You don't necessarily want "self-improvement". Improvement is a vector; you need a direction. You should focus on the scalar aspect, moving around, without direction.

All religions start off tackling spirituality and morality. Sit and think about everything and you have Buddhism. Focus on relationships and virtues and you have Confucianism. Focus on second chances and forgiveness and you have Christianity. Focus on serving a single dominant God and you have Islam and Judaism.

You can and should explore all of these, at least on a surface level. There's a lot of good ideas out there and people have literally sat around their whole lives debating and refining these ideas. Ideas that are not good tend to get lost to time.

There's a popular painting, The Vinegar Tasters, which depicts three men tasting vinegar representing life. Buddha thinks it bitter. Confucius thinks it sour. Laozi thinks it sweet. As a pseudo-religious, you could be unattached enough to understand and appreciate the perspective of these men.

Why not do all of them, understand why all religions are what they are. Religions are developed over thousands of years. Cults usually revolve around a common mystical experience. Religions often successfully translate that experience into a book and replicate it hundreds of years later.