QA -> PO shift

Hi, I currently have 5 YOE in Quality Engineering in a Scrum/Agile environment, so I have closely seen what POs do and have also gotten the opportunity to shadow POs. But my company is not supportive enough for me making the shift, so I’m trying outside and I have been unsuccessful till now.

Trying to understand where I am going wrong or if these PO/PM roles just do not hire without prior PO/PM experience on paper.

Is PO/PM a dying career ? Should I not be getting into it ?