This is a halakhic, but I will admit, also midat chasidut question. I understand the Rosh Yeshiva has often pointed out leniencies about the halakhic status about today’s bathrooms. I listen to shiurim on headphone around my home. If I’m walking into a clean bathroom for a moment, must I pause the shiur? Would it actually be wrong to specifically pause a shiur in that moment? Same for walking in for a few minutes, say to find something in a cabinet or to quickly tidy the space.
You are correct that today’s bathrooms do not have a status of a בית הכסא. Shulchan Arukh OC 83:4, following Berakhot 26a, rules that if the actual site where the waste comes to a rest is 4 amot away from the opening where one relieves himself, and the waste rolls away immediately, then that space where one sat does not have a status of a בית הכסא. Our bathrooms are even better than this, as the waste falls into water, so it does not dirty anything, and it washes away very far. See Piskei Teshuvot 83:4, and footnote 17, who cites many Achronim who deal with this. The upshot is that they acknowledge that as a matter of halakha our bathrooms do not have the halakha of בית הכסא, but nevertheless, for appropriateness, or because the waste stays for a minute and sometimes doesn’t fully wash away, one should treat them as if they are a real בית הכסא.
I think that the matter is more subjective. I feel that since we do identify this room as a bathroom, and from a feeling of appropriateness, most people, for example, don’t eat there, having nothing to do with halakha, then we should ask ourselves, what does and doesn’t feel appropriate from the perspective of divrei kedushah and a non-halakhic bathroom. For me, at least, bringing a Gemara would be inappropriate, the physical reality of having a Gemara in a place designated for relieving yourself feels wrong. On the other hand, something which is not visible or heard to the outside world, such as thinking about Torah or listening to a podcast, to me feels less problematic, since you are just going in and out. Perhaps staying there for a while to tidy stuff up would be more of a problem. You must make your own judgement about this.