My 12 yo with dyspraxia, hyper mobility and autism really struggles with cutlery and table skills. It's a tough combination as fine motor control is tiring and often painful to him. The autism element makes him resistant to change and criticism, especially when he's hungry, but he has no interest in practicing skills when he isn't. Rather than triggering a meltdown every meal over the finer points of dining, I focus on the easy wins; sit, use cutlery, no knees, feet out of sight, close mouth when chewing. Generally no phones, although if we are out, occasionally it's to the greater good to let him zone out if there's a risk of a meltdown. We tend to avoid places with prolonged waiting around different stages of a meal, so for us, a carvery tends to be a nice meal out.
The key bit is that despite appearances, he's been taught, and eats at a table at pretty much every meal. For a start, I like my living room too much to risk soft furnishings with gravity-defying food.
Most manners originate with some kind of purpose, and generally have a right-handed bias. Knifes often are serrated to the favour of use in the right hand. In cultures where hands are used, there's ettiquette like "eat with the right, wipe with the left" originating in hygiene again favouring right-handed people. There's ettiquette in where to hold your chopsticks (I thought I was doing well but apparently I hold them too low and am low-class) It's good that diversity like being left handed is no longer being spanked out of people in the UK over the last few decades but we're not in a cultural vacuum either. I don't mind if people swap their cutlery/ glasses over for comfort, but knowing how a table is laid is useful because it stops people taking the wrong items at a group meal and leaving others sourcing the spare items from around the table.
Letting a child grow up with no culturally relevant manners is a social neglect. Not being prompted to use cutlery either means that parents haven't put much effort into developing a child's skills, or their diet is pretty limited if it can usually be done with finger foods. OP is limited in what she can introduce successfully if the girl's parents haven't been paying much attention. Setting an example may help if OP has a healthy relationship, but much more than that is likely to meet resistance in an older child, and the cost of that is high.
It is possible that a condition like dyspraxia has been overlooked, but there would normally be other signs such as poor hand writing, slow writing speed, difficulty with tasks like shoe laces, maybe gross motor control such as throwing/ catching, being one-sided with movement (DS can only scoot single sided) difficulty with skills like swimming or cycling. Diagnosis can be tricky to get- ours emerged during private dyslexia assessment, there is no public assessment in my area so only families with spare £££ can be diagnosed if they know enough to recognise traits.
Neurodivergence needs accommodating, but parents are responsible for teaching table skills in the first place and are letting their children down if they never even attempt to appropriately develop them in the first place. Schools often don't pick these things up, and are often limited in what they will be preapred to see and do even in diagnosed children.