Please don't worry! I teach Reception and all the areas she's 'emerging' in are typically the most common areas for children to struggle with during the Autumn term.
Obviously I don't know your child to know whether she's only slightly behind the expected level in each area, or whether she's way off, but a child will only be marked expected in Autumn if their teacher is 100% sure they will get there in June, when end of year data needs to be submitted. Any doubt at all, even if just a slight doubt, you go for emerging and put in interventions to ensure you're giving that child the best possible chance of getting there. Teachers want to show progress. I totally understand why it worries parents to see 'emerging' at any stage but it's only a problem if they're not expected in June.
There is still plenty of time for her to reach the expected level even if she's quite far off it in some areas at this stage, as children 'click' at different times (especially with the reading and writing). It's so common for children to struggle with these areas in the Autumn term, then suddenly 'get it' by February/March and reach 'expected' fairly comfortably by the end of Reception. Speaking too is generally a weak area in the Autumn term in Reception but one which improves a lot as they develop greater confidence and vocabulary. Comprehension is largely based on their vocabulary too, which will be improving all the time.
The main things that stand out for me are that her effort and behaviour are good so that is something to be very proud of and will stand her in good stead to have improved by the spring term data drop. Her PSED is also at the expected level, which can be the main barrier to some children's chances of progress, so I'd say the signs are encouraging.
I really wish schools wouldn't do these termly reports in Reception as the wording panics parents unnecessarily. I'm sure if her teacher had any major concerns she would have raised them in person right now. Honestly, I understand your concerns but many of my own class have data which reads like this right now and I know deep down many of them will reach expected by June, they're just not there yet.
If you don't already, make sure you're reading every day and talking about books in general. Talk to her about her day, modelling full sentences and the flow of a conversation. Everything will start to click into place when she's ready.