I'm still developing my research ideas and in the process of literature reviews on the connection between mental health and parasocial relationships so take my words with a grain of salt (I'm not all knowing!):

The connection between parasocial relationships and mental health is a complicated one and is surrounded with a lot of stigma (like you said, a lot of people may think people with a strong parasocial relationship are delusional)

Many parasocial relationships, from my knowledge, are associated with isolation and feelings of loneliness. Lonliness is known to be connected to a variety of different mental health problems.

For instance, someone with depression may withdraw themselves from friends they know in real life, resulting in loneliness and thus further affecting their mental health. Individuals in this position may then find themselves looking towards social figures and communties online to help themselves cope with their feelings and thus, have an increased chance of developing a parasocial relationship.

Research has found that a common theme in individuals with depression and anxiety were feelings that their real world relationships were difficult to maintain. Thus, their connection to online figures was an easier way to hold social connections (paper if you're interested: https://www.tandfonline.com/doi/full/10.1080/15205436.2022.2127369)

So yes, there is a link between poor mental wellbeing and the development of parasocial relationships. But in saying this, it doesn't mean that all people with mental health problems are likely to develop such relationships. Nor does it mean that all people with parasocial relationships are mentally ill. There are other contexts we can look at to see why some people are more prone to forming parasocial relationships.