T5 government authorised exchange visa or graduate visa

Dear All

I need you help. Recently, I have secured a job at one university in the UK. However, this job is from an approved government authorised exchange scheme, and the Chinese government-related institution in the UK will be my sponsor rather than the university. Although I will work in the university, from the UK government's website, it mentioned that the role is not filling vacancies.

https://www.gov.uk/government-authorised-exchange

Right now, I have a graduate visa for two years which can allow me to do most of the jobs in the UK (including this one of course), but this time, the university still asked me to apply for the government authorised exchange visa as they said they are not the sponsor and afraid to breach the immigration rules. Is this sure?

Can I work as a temporary worker with graduate visa? Can I ask the university to send me a confirmation from UKVI about the regulations? as you know, T5 visa does not count towards settlement or ILR.

Many thanks for your help.