(Sorry this took me a while to write, so I can see there have been new posts in the meantime).
I think four is such a tricky age because they seem so grown up, articulate etc but then their behaviour really doesn't match a lot of the time and it can be really confusing. Especially when they have moments of seeming so lucid.
When my (giant, hulking) 16yo was about 4 I really struggled and I remember reading a comment on here. I can't remember if it was my thread or somebody else's but the poster wrote "At four they are still babies really." It stuck with me somehow. And with the perspective of hindsight (I have DC 16, 6, 3) - they were right. Four is SO little.
At the same time it's kind of a middle way thing - you can't do too much for them or they just expect you to do it all the time.
My 16yo and 6yo have ADHD and one aspect of this is that their executive functioning skills are delayed in development. So I've ended up looking into this a lot and the typical developmental timescale of it and actually - I do think sometimes we (parents in general) tend to skip stages of this unwittingly. It's not a blaming thing to say that because I honestly wouldn't have had any idea had I not looked into it.
BTW, I think from your description she sounds exactly where she should be, and she is probably tired from working so hard at school. You could try a multivitamin containing vitamin D and C, this might help her energy levels. And try to make sure she has chance to rest and sleep enough.
I would ignore a lot of the annoying behaviour immediately after school like nose picking or answering back. Or see if you can diffuse with humour. Whatever you do, don't play into it by getting annoyed by it - it's likely that she already knows this is not acceptable behaviour and that's exactly why she is doing it, which also means that it should dissipate by itself once she is less tired and moody. Also, bring a snack to pick up, like a cereal bar or a piece of fruit or some rice cakes.
Talk to the teacher about homework and what their recommendation is. In some schools in reception, it's optional, or it's there to help set up good habits, if it's causing further stress then they may say not to worry about it. Other times the teacher feels very strongly that it is important to keep practising the skills at home - there might be a less-pressured way you could do that e.g. songs or games. Or it might work to put a time limit on homework so work on it for up to 20 mins and then stop, for example. Or they might say please do the reading but don't worry about other homework. It is likely better to read one page of a reading book and have this be a positive experience for her, rather than push her to read the whole book but it take an hour and be stressful for everyone.
Another thing you can do with homework is experiment with the timing of it - is it any easier to get her to do it e.g. on the way home (if it's a 5 min app) or as soon as you get back, or after a snack, or before dinner/after dinner, or at some other natural pause e.g. while waiting for a sibling to come out of their class/activity. And understand as well that it's totally normal for her attention span to be completely diminished after a day of working hard and sticking to the school rules - think about when you've started a new job, you tend to be totally drained by the evening and not able to concentrate for long even on something you enjoy.
I can get a bit more concentration out of DS2 as well if I get him to do something active first like bouncing or a "brain break" type dance from youtube. I don't think that's just an ADHD thing - I think it would probably be helpful for a lot of young children. Even adults sometimes wake themselves up with a walk around the block or some exercise. Letting her know that the exercise will "rejuice her brain" can help even if it's a total placebo effect - it might let her concentrate for enough time to get it done.
I tell her to put things away and she leaves them on the floor and then stands on them, they get broken. Yes a natural consequence but she doesn't remember for next time, even when reminded
That is a good example of where I think we often have too high expectations for 4yos. It's unlikely this consequence will help her remember, it's too far removed from the behaviour. If you want her to put something away, you need to be really close to her (ie within arm's reach, ideally even with a hand on her to ensure you have her attention) when you give the instruction and basically guide her to do it, then lots of praise when she does. It helps if it's a routine too, as she will do it more automatically then. And try to set her up for success e.g. for after-school coats and shoes, make the storage accessible and not overstuffed, or if she is pulling out 20 things to get to the one thing that she wants, try rearranging her storage and/or cutting down on the amount of stuff that is there in the first place - it might be she has a lot of outgrown toys/books/clothes/etc she no longer uses which are getting in the way.
What time is bedtime, and what time is she typically falling asleep?