I'm not in NYC and my district put into their school board policy around the same time they started giving all students in grades 7-12 a laptop that all teachers will post all assignments online. Checking the assignment book was a thing with my oldest but it wasn't needed with her younger brother with the change in policy. They even made assignment books optional for all students when they made this change.
If K-12 is getting students ready for college, I'd say that 99.99% of colleges have their assignments posted online.
My other thought is: are teachers posting the assignments on the portal when they are assigned? If they are, you & your child could be checking the portal to see the assignments. Pretty sure our portal said if the assignment was an in-class assignment or a homework assignment. This could also be an IEP accommodation: Teachers will post all assignments on the school portal when assigned or they much check student's assignment book that all assignments are written in the book.
Like Carolyn said: teachers need to follow the IEP. If they are supposed to check the assignment book & it's not happening, they are out of compliance with the IEP. The solution is to go up the chain of command or file a state complaint. You can also do both & file a complaint if talking to the school isn't working.