Either could come out of my mouth, and it’s not for particular situations, just a roll of the dice.
Theoretically there could be a logical reason for a possessive pronoun to avoid ambiguity but it’s a stretch. If you work in a small office, are asked about lunch plans, and say “I brought lunch today” it could be construed as meaning you brought lunch for everybody, whereas “I brought my lunch today” means “I got mine, you’re on your own”.
Language isn’t logical. That goes double for conversational language.
Mine are generally unposessed, but I’ve known people to use those possessives. I think the possessed meals are emphatic: the question isn’t so much “did you eat something” as “did you eat that specific thing”. Note that other things which are also ingested do carry possessives: “did you take your medication?” or “now where have I put my drink?” have very different meanings from “did you take medication?” or “now where have I put the drinks?”
When I was taking French in high school, we learned that the phrase “to sleep in” in French was an idiom: “faire la grasse matinee.” Translated literally into English, that phrase means, “do the whole fat morning.”
More the latter, I imagine. The literal translation of the French idiom has always amused me, and this thread had reminded me of it.
Also, getting back to the topic of the OP, from what I remember from high school French, the term that we were taught for “I’ll have [food]” in French is “I’ll take [food],” which always sounded to me like taking drugs.
Look, when I say that “it seems unnecessary and odd,” it means “it’s not idiomatic in my dialect or idiolect.” I don’t need an explanation of what an idiom is, just your own experience using or not using that syntax or noticing it from the people around you.
The OP is talking about something called an affective particle. All languages (it is likely) have ways to encode affect, and in some it is more formalized than others. In English, we use possessive adjectives as affective particles in certain contexts, and that’s what’s happening with Ascenray’s wife although I can’t speak to why she would be doing it in this case. (It might be a regional adoption.)
To clarify with English, it’s similar, for example, when you’re upset with someone, and you use the affective particle to belittle something they’re doing:*Go ahead – have your party. I didn’t want to be invited anyway!*In this case, it’s a possessive adjective, and it encodes contempt. It’s important to note that the same kind of marker can show varying stances, because these particles are highly idiomatic in English. Ascenray’s wife may just be encoding familiarity with him by using the possessive adjectives in this way.
Another example of a different kind of affective particle is when someone comes to visit you, and you meet them at the door. You can say:
*Come in!or you can sayCome on in!*In this case, on is an affective particle to show friendliness and a welcoming stance.
English is a particularly particulate language. Some languages use composite words where English uses particle assemblages, and some of them make little sense. Like the verb “put up with”, which cannot be deconstructed in any sensible way. Or there is “soldier on”, where “soldier” is not a verb in any other usage. Of course, many other constructions do make better sense (though “of course” is pretty baffling).
I mostly hear the possessive used for meals in two situations. One is to eliminate ambiguity - I “bring my lunch” to the office because if I say I “brought lunch”, it’s likely someone will think I brought lunch for everyone. The other reason is for emphasis - I often hear people at work say something like “It’s two o’clock and I haven’t had my lunch yet”.