Hi and welcome to BW
How about just passing her the spoon with the puree on? Or one spoon for you and a second spoon for her?
At this age (and younger) my DS liked to use a fork, I pre-loaded a plastic fork and handed it to him or left it on his tray for him to pick up, initially I held on to the end of it to prevent him poking himself in the face, but he was in control of self feeding and enjoyed it.
I notice you say you are cutting up her finger food into small pieces. Is she proficient with a pincer grasp (using thumb and finger to pick up small objects)? Some LOs have developed this skill at this age, others not, so you might be making it more difficult for her to self feed by cutting food too small.
How about trying some large wedges or finger foods - for size use an adult finger as a guide, this way it is large enough for her to pick up in a fist grip, or for you to hand to her, she has enough length of the food to hold in her fist with a little poking out of the top for her to chew on.
Similarly chopped banana can be super slippy and very difficult to pick up, you may have more success with handing her the entire banana, or at least a half banana, the outside tends to be 'drier' and easier to grip (until it's all mushed up with the gumming and gnawing!).
Do you eat at the same time she eats? LOs love to copy their Mummy so if you can sit with her and have the same meal this is super encouraging. First she sees you are eating the same food, then she sees you are enjoying it. At 9 months she can eat pretty much anything (a few exceptions are honey, whole nuts, keep salt to a minimum) so perhaps she'd like to join in the family meal rather than have a different looking puree meal? She might surprise you by enjoying some meat or fish, or some spaghetti which isn't pureed, or some baked sweet potato wedges (baked or roasted tend to be nice and 'dry' on the outside, so easier to pick up, but very soft inside so easy to gnaw on).
I think on your other thread you mentioned teething, LOs can go off their food whilst teething of course, so just keep offering and she will eventually take more foods.
hth
