A court hearing against my current visa sponsor. How is the UKVI going to consider this if I mention it in my FLR application?

I may have a court hearing at the Sheriff's court in a very serious civil matter where I m the Pursuer, in the next 60 days. It's an Ordinary cause action against my current sponsor which is a University. I am done with the internal complaints team and the Ombudsmen. The latter told me last month that they can't complete their investigation before my visa expiry.

I want to be in the UK to fight this case which entails deliberate misrepresentations, major service delivery failure, negligence and administration failures etc., however, my visa will expire in a month's time.

Is this going to assist my FLR (O) or FLR (Private route) visa application in any way or should I not bother mentioning it there? I am not filing the case due to any visa extension. The situation just happened and my claim is very high.

I have also made Home Office as the second party in my writ petition which I an planning to submit soon. Is that a good idea?

I am afraid the Home Office may react to it negatively so I shouldn't mention them at all in the writ. However, I m also thinking the initial receipt produced by the Sheriff's court and the judge's initial standard order may assist.

In your perspective, is the Home Office going to give the above any credence or should I not mention them at all in the initial writ?

Kindly advise and state your charges for doing an FLR application.