Writing is part of RWI lessons (some schools choose not to do the writing part, however) but it's not assessed on the RWI assessment. To progress from Yellow to Blue, your daughter needs to be able to instantly recognise the first six Set 3 sounds (ea oi a-e i-e o-e and u-e), as well as the Set 1 and 2 sounds she's learnt before (she will have needed to know these to get onto Yellow in the first place). She will also need to read words with these Set 3 sounds in, and read a passage from a Yellow book at 60+ WPM. The passages in the assessment are all edited from the Yellow books she'll be reading - the one I've attached is from Book 6 "Do We Have to Keep It" (one of my faves!). I've attached an example of the words and the passage, as well as the assessment guidance listing what children have to do to move up into Blue group.
It sounds like because she hasn't moved up, but lots of children have moved up to Yellow, they have gone back to the beginning with the books because they tend to get harder as you go along. If the group was mainly comprised of children who had already been on Yellow, they probably would've continued from where they got to.
I would see if you can find out what it is she's not doing that's preventing her from moving up (sounds, words, or speed) and work on that a bit with her at home. I suspect it's speed - children often get stuck on Yellow because it's the first stage that includes a timed element. But also make sure she's got access to other things to read so she's not getting bored of the same books all the time. See if you can sell it to her as a chance to show off and be fantastic at those books because she's already familiar with them. I would imagine re-reading will help with her speed, and she should move up at the next assessment if she's been making steady progress to this point. Yellow at this point in Y1 is a little ahead of the curve anyway.
Just seen your question about books - there are books they use in class, and each one has a matched book bag book sent home. So if they've read The Gingerbread Man in class, they bring home The Hungry Fox, which features the fox sniffing out different things to eat but finding nothing smells as nice as the gingerbread man did. Since Covid, most of those books are available as PDFs on various school's websites - just google the name of the book and "RWI PDF" and they come up. You can also find a full list of all the RWI books by googling "full list of RWI books" - it's the first hit. Children should bring home a paper copy of the book after they've read it in class so they can read it at home, but some schools don't do that because they don't have enough copies/they find the books don't come back.