Lonely is a neutral connotation because lonely implies that you are alone like when used with lonely boy which says that the boy is alone which isn't bad, but isn't good.
unlonely - Negative
Rejected has a negative connotation because rejected is used to say that you were said no to and left in the dust. In the sentence "Your rejected soul" the speaker implies that the soul is a bad soul and is hevily disliked
loved - Possitive
Uncherished has a positive connotation it is used like uncherished child or uncherished soul states that it is not their falt but other peoples falt
Popular - Neutral
Unlonely has a negative connotation because unlonely state is a state when you are with another, but you are not close or mabey not even comunicating.
Loved has a possitive connotation. People asociate loved with being with someone that you care for and enjoy being with.
Popular has a neutral connotation because in today's social media, you can be popular for a good reason like saving a cat, or a bad reason like stealing from target.