It's common to say 吃饭 (eat rice) as a way of saying "to have a meal".
Unsure what it is supposed to mean in this context though.
(note: also don't trust a random person on the internet - me - with your translations)
The use of "tea" for that meal remains a class signifier; my paternal grandmother used it, my parents did not (my mother, despite not being a native speaker, presumably is the one who eradicated it from my father's vocabulary), and yet I continue to say unwittingly say it occasionally though I now live in the USA. A vestigial Australianism in my case
It's definitely "non-U" in the UK, though that whole world is mostly gone.
However, based on my research (1), "扒饭" is likely a meal type rather than an action. For example, "鸡扒饭" consists of a bowl of rice covered by a layer of pre-cooked chicken breast plus some veggies. The rice itself seemed normally cooked, not grilled. And yes, this sounded very similar to "盖浇饭" which is also a meal type.
1: https://duckduckgo.com/?q=%E6%89%92%E9%A5%AD&iax=images&ia=i... yes, quite literally a re-search
(Me been a local to the country, you would assume that I knew this kind of things. Well...no, this is the first time I learned this term. But if someone asks me "Hey do you want some 鸡扒饭?", I'll take my chances.)
Note: 排 literally means ribs. But this dish has been evolved quite a bit and now 猪排 could be any part of pork, and I'd say pork chop is actually more common than actual ribs nowadays. Same goes to chicken - 鸡排/鸡扒 is typically just chicken breast (not like chicken has ribs to begin with, hehe).
So like “break bread”, “earning bread”, “bread and butter” etc.