I haven't found any great evidence or research that definitively states why someone should or shouldn't drink when eating post surgery. I think you can roll with whatever works best for you as an individual and be okay. I personally, will have a drink up to the point of my meal. I don't drink during my meal, and I usually wait until 30 mins after, but for me I feel more satiated longer when I don't drink right after. If I drink with the meal and immediately after (I've experimented on myself to experience the difference), I seem to get hungrier earlier, before the next meal.
That's just me though. I don't think that's what everyone should be doing. Just like the food we eat, once we get well into "normal" eating, we've got to figure out what works best for our individual system and what will maintain us for the long term. There is no one diet or order of eating that's going to apply to every single person. There are some basic tenets to follow, I think, but in general, two people could be doing wildly different thing and both experiencing great success.