My first fed to sleep for around 4 months and was the only way he'd sleep, it took some perseverance but he got out of the habit and became an excellent and independent napper and milk had nothing to do with it. Even at bedtime. So please don't worry.
@Sophie out of curiosity, did he got out of this habit by himself or you had to make the change?
My baby is pretty much the same. Sometimes it will be eat/play/sleep while others play/eat/sleep. It depends on how long he slept actually and if he is hungry when waking up! They suggest that so they will not associate eat with sleep, ie feeding to sleep. I would say if it works for you then it’s fine.