I am curious as to whether there is a noun or some other, more suitable expression for that group of people which shares my personality type. I often use 'people with same traits or personality'.
It is more general than personality type but it fits somewhat:
possibly clique or coterie
I can't comment so I have to write it in an answer
"Birds of a feather (flock together)"
The best word I can think of is peers.
- one that is of equal standing with another : one belonging to the same societal group especially based on age, grade, or status
- a person who is equal to another in abilities, qualifications, age, background, and social status
Peers could refer to anyone who shares your personality or otherwise "belongs to the same group", regardless whether they are actual acquaintances of yours.