EU, post PhD and 4 yrs research support role in life science, is a career shift realistic?

I am a PhD and have been working in a research support function role for the past three years. I started in medical communications, at a consultancy hated it. Moved to technology transfer in a university for two years and now in a similar role at a research institute.
Tech transfer team here is new, I am the first here with no team lead or any team member- it has been a year already. So it has been very unstructured and difficult to navigate. I constantly feel like I don’t fit into the research context and am not taken seriously; not having a team lead is not helpful here. Taking initiative here is difficult; I also acknowledge the possibility that I probably did not exercise the option of asserting and leading (“seizing the opportunity” - which I find very difficult in this environment).
I am starting to realise that academia as a context and this role is perhaps not best suited for me. I don’t see growth or challenge. I am constantly frustrated at inefficiencies.
I am very often complemented on my transferable skills which I believe are strong and under utilised (communication, networking, structuring a problem, strategising, to name some) but I find it very hard to “transfer” them out of academia.
I have considered doing an MBA or some other course but there is a fear of being over qualified and under experienced in my early 30s.

But there is also a very strong pattern that I question- is this a wrong career field or is my approach to something wrong; am I impatient? And for my profile is a career shift realistic and is the hustle even worth it?

Any pointers would be helpful. Thanks!