It really isn't the role of OH to advocate for you to have management support. They will recommend a stress risk assessment and possibly a wellness plan and both of those are conducted by the manager. If you were to agree, they might note that you feel your issues are trivialised and you would prefer those meetings to take place with another manager, usually the manager's manager. Only you can know if that would be helpful or if you would veto the report. If the latter, it's all a bit pointless isn't it?
Whilst I think it's poor practice to insist the report can only be raised by the manager as there are sometimes confidentiality issues most adjustments have to be implemented by the manager and two way channels of communication are important.
If there is an issue with your manager, can you speak with their manager to try to seek a resolution?
If you are managing the team that won't or can't work, what evidence do you have of their non compliance? Notes of 1:1 meetings, performance reviews, standard setting, etc. I do realise that toxic teams exist and they are very tricky to turn round.
Grievances are rarely successful. They fracture already brittle relationships and mostly recommend stuff that minimises risk for the institution: mediation, training, 1:1 meetings, etc. Rarely a cultural review. If patients are suffering you could of course blow the whistle but I suspect immense strength and resilience is required for that.
If this has been an ongoing issue for a number of years then leave. Transfer to another dept or provider. No job is worth unhappiness. Tell them in your exit interview.
It's hard to say from the outside and with limited knowledge. It may be a distinct pocket of toxicity impacting patient care, and there have been enough to reach the press to know they exist, or it may be that you are a square peg in a round hole and would do better elsewhere.
No job is worth years of unhappiness. From what we are told the NHS has vacancies everywhere so apply fir one and see if somewhere else is different.
Good luck