Advise about funded nursery hours

My 2-year-old was due to start nursery using her funded hours on 1 October. She had been doing settling-in sessions of around 9:30am–1pm, which she seemed to manage well. Her planned hours were 3 days a week, from 7:30am to 1pm.
However, I still haven’t heard from the nursery about a start date, and I wasn’t billed for October, so I’m worried that her start may have been delayed or that there is another issue.
The main concern is that she has been refusing all food and drinks while she is at nursery. Once she comes home, she eats and drinks perfectly normally, so this seems to be specific to nursery rather than a general loss of appetite. She otherwise seems settled and not distressed while she is there.
She is currently on a pathway for a possible autism diagnosis, and I’m worried that the full 5.5-hour sessions may be too much for her at the moment. I would prefer 3–4 hours a day, so she could still benefit from the social interaction without becoming overwhelmed.
I’m also worried that the nursery might defer her start again, as they already did when she was one. I’m concerned they may not only defer her but could refuse to take her altogether because she is not eating or drinking there.
The manager said she would speak to the area manager about possible options, but I haven’t heard back yet.
Has anyone had a similar experience? Were you allowed to use fewer funded hours or arrange shorter sessions? If you couldn’t afford to pay privately, did the nursery offer any alternatives or a gradual transition? Did anyone have a nursery refuse or defer a place because their child was not eating or drinking there, even though they ate normally at home?