Op I work in childcare and have potty trained hundreds of kids over the years.
I don't think you're being unreasonable to expect the nursery staff to remind your ds to use the potty and to assist him with this
I do think you're being unreasonable to get angry and blame the nursery staff for your ds having accidents. Yes, even 5 can happen when we are setting them on the potty ourselves and sitting there with them, encouraging them to pee.
Nursery is very different to home. It's much busier, louder and some children do struggle with using the potty at a setting compared to being in the familiarity of their own home.
Trust me, the staff aren't enjoying your ds wetting himself and having to change him every time, I doubt they are letting him do this on purpose.
Sticker charts are usually quite effective with young children, so maybe santa could bring some and he can take them into nursery and get a lovely shiny sticker if he manages to do a wee on the potty. Nursery staff will make a huge fuss of him and he will feel good about himself.
I know it's frustrating, but you're going to have to just be patient, relax and not make a massive deal out of it. He will get there, and will be there long before he is 6!