My pet peeve about this trope as a Philologist is that while I (kinda) wish people spoke like this as I love listening to different languages, accents and idioms, it definitely doesn't happen in this sense and the lack of research, or worse, deliberate ignoration of this as OP says shows 😂😩 Like I'll cuss you out in one of my three main languages, for sure, but to get there you'll have to defeat my 7 levels of perfectionism and gifted burnout child vocabulary reserves.
Yes I'll definitely use a word from another language instead of the correct one if i cannot remember it in this one we're mutually using, but I will not be spewing catchphrases like an NPC.
Do I still eat the trope up? 100% (I mean Jackie Welles Cyberpunk2077 hello-)
The irony also applies to pet names and terms of endearment. You're unlikely to use that many L1 terms of endearment on a loved one that doesn't speak said language (though some consciously choose to do so, whether due to sentimentality or as a form of flirting), and unless you're in a movie or carefully curated, slowburn fanfic, you'll be settling for more common terms, usually in a language you share. You'd more likely have to be limited by a lower level skill in L2 to resort to L1 phrases when you're at a loss of words, or rather overwhelmed by other factors such as emotions; and someone with other languages in their arsenal will compensate for this lack with one of them, not necessarily his native tongue, esp if it's rarer, such as in my case where the counterpart most likely still won't understand a fundamentally different word from Serbian or Greek for example.
One instance where I can imagine this bilingual conundrum working, is in creole or pidgin languages*. Languages meant to function in a multilingual/multicultural environment, or ones that are based heavily on such linguistic development, are more likely to mix terms and structures, producing their own in turn. Notice how these OP media tropes don't often happen in "less popular/romanticized" languages, either. We'll see a lot of French or Spanish terms thrown around for pet names, as they're notorious for romance settings, or perhaps some popular foreign slang that's been meme-fied on the net by other, less "romantic" languages. That's where these stop though, don't they?
Somehow Gambit calling you ma chér in French makes more sense when Cajun actively uses it in anglophone environments too, while Bane calling you a million spanish endearments while he's a genius fluent in several languages, can only be doing it for the love of the game (this man is an expert in psychology amongst other things, he knows the effect a nice little Cariña has on you) 😆
*my knowledge of creole and pidgin language structure is still small compared to others, this is a personal assumption with data gathered thus far
