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.
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)