I grew up with a family suffering through immense generational trauma all my life; my uncle died at only 14 and it fucked up my grandparents and mother's mental stare permanently, understandably so.
Their relationship continued to sour as decades went on, and by the time I was a little boy nothings improved, if anything it only got worse as my autistic fucking horrid sister made our lives so much worse. My family used me for financial gain, insurance and credit card fraud, and treated me like utter garbage despite it.
Eventually, I grew so tired of it, the violence, the anger, the rage; I called protective services and left home that day. I have no regrets leaving, except for one thing: leaving behind my stuff, which DID include plushes.
As a 22 year old, I've got many many plushes. I don't think plushes as an adult = trauma coping. I think anything you may become attached to, especially when stripped away, becomes an outlet to cope with trauma. I lost all my transformers too; well around 400 figures, and I left them behind for my own sake. I miss them dearly, even as I collect new figures to this day. And thought this may be the case for some, as others have also shown here, its not always the case.
Plushes are likely just used as the prime example since they're soft, cute, huggable, and often associated with childhood and young life.