In my experience it varied by child. Dd1 absolutely refused to read at home so was listened to at school 3-4 times a week during the months of strike. School were very supportive. She finally gave in and became fluent soon after.
Dd2 struggled with reading and I think she would have benefited from more time at school as well as at home, she had 1-2 times a week often in guided reading.
Ds was listened to very rarely. I made it clear early on that l did not expect him to be a priority in class he read and could understand Harry Potter and The Hobbit in reception. I saw no reason for him to have extra time reading when children like my dds were struggling. It was in his interests too that the rest of the class caught up with him. He will happily read for ages by himself at home and reads to us every night. We are able to discuss the pronounciation and meaning of words and google any we can't explain just as well as a TA or teacher.
In terms of reading material I have been somewhat rebellious. I have found that once they reach a certain level they are much happier following their own interests than reading 40 year old school books. Nowt wrong with classics, but we have probably all encountered the sort of books I mean. Once they can read fairly fluently (old ORT levels 11/12) then many books are available to them. I have been fairly open in my refusal I have made it clear that I don't mind what they read in school (within reason) because I understand that in guided reading they need to read as a group, at home though they won't waste time read books which don't interest them so we will provide our own. If they wish us to then we will write down what we have read together in a reading record. To the children I have just said that we don't need the boring and sometimes inappropriate school books because we have lots of our own and would just lose them they all know my mad library book dance .
I should say that the only one who enjoyed the repetitive chapter books was dd1 and with her we would give anything (even Rainbow fairies) to her if we knew she would read it. For the others reading books have varied between atlases, encyclopedias, star wars 'information' books, Harry Potter, Narnia books, David Walliams, Enid Blyton, etc. Basically anything that they find interesting but which challenges their reading ability sufficiently.
If your son is fairly happy and confident reading then you will probably do a better job (as long as it isn't an area which you struggle with yourself) than a hassled TA grabbing 10 minutes whilst the class rage around them. I would just refuse to have school books if they still send them home then just write 'Harry decided to read war and peace instead of Biff and Chip find another magic key tonight, he read 15 pages and we had a good discussion about the term vexatious'. Substitute as appropriate. Have confidence in your ability to know your son and to support his reading adventure. He probably won't thank you if you try to get his teachers to make him read the same boring books even more often at school. Especially if there is no new vocabulary. Sometimes they will take in a book from home and the teacher might listen to them read that.