Your poor grandson! Anxiety is awful, it's crippling and it can end up taking over- and limiting- your life.
I have no experience of ARFID, but I was a very anxious child. I grew up with my mother telling me to "be careful" and "don't do that, it's dangerous"... it sounds like such a little thing, but as a child, you believe everything that your parents/carers/close family members say.
Does anyone in the family suffer with anxiety? I have a few in my family, which ramped up the pressure on me to not be a "failure" in their eyes. If the eldest grandson is anxious, it's likely that it will rub off on his brother, so that needs to be carefully managed.
Does he have any issues at school? Is he being bullied, or is the school environment just too much for him? Would a smaller school be better for him? Is he doing long hours, e.g. breakfast club, school, after school club and then extracurricular activities?
Don't dismiss his worries or anxieties, e.g. telling him to, "Shut up and stop moaning" (i.e. my family's attitude). Talk them through, watch other people doing "dangerous" activities, watch close friends or families riding bikes or something, so that he can see that they are doing it safely. Would he ride a bike with stabilisers on, or a tricycle? (I realise that they're unusual, but I've occasionally seen adults on them). That way, there's less worry of falling off, but he's still exercising.
Give him time to calm down and decompress after school/activities. Find out whatever it is that makes him feel safe and calm. Try to avoid putting so much pressure on him that he stresses out. Is there anything that he could do that might raise his confidence? (E.g. Cub Scouts usually do a mixture of safe and "dangerous" activities, such as climbing walls).
I'm not sure if anyone at his school would be able to help, but it's a start. I'm unsure if a GP would be of any use to someone so young, but is there any chance of a CAMHS referral?
I hope that lots of other people come along with useful suggestions, OP. I hope that you and your grandsons have a good week.