Like @Natalie said you are doing amazingly, it is a new environment for her and like you say you have 3 languages in the home that will definitely take her some time to catch up on and talking to others, especially in a busy noisy nursery setting with loads of conversations going on rather than the usual home setting. a HV is always a good idea to help you see and realise what you are already doing is great and they’ll just give you pointers. To be fair our nursery told us our lo wasn’t eating only when they were feeding her themselves and they thought we were doing that at home..shocked mum here (she’s 2.3 months too!) cue me sending them a video and a photo to let them know she does this at home very well without me intervening and is very confident with eating with cutlery so they put it down to her confidence and again like Natalie said her safe space at home. I’m sure in a few more months she will come along fine.
It could just be an adjustment period for her. When my son started nursery they were concerned that he didn’t play with other children, wasn’t saying much etc and they even wanted to offer 1:1 support for him. Now he’s doing really well but still not eating much while he’s there. It’s a very big change and it takes time to adjust and if they never do the n it might not be the right nursery for them.
You aren't a bad mum at all. Sounds like home is her safe space so she feels more confident to do things there/when around you which is completely normal especially when she's only been going a very short time. My daughter has been doing loads of stuff at home that nursery have never seen. We had a parents evening where they said we are working on counting and I asked her then she counted to 10 cos we were present. Nursery can only go by what they see when tracking her development. Could you show them videos of her doing some of those things at home? Some nurseries will use that for an observation and include it. Others won't. Nothing to worry about with the health visitor coming. They just want to see if there is anything you need support with. They wouldn't want to not come/nursery wouldn't want to not make a referral when someone actually does need support or the child is behind. Sounds like you are doing amazing!