If you're planning to apply to graduate school in the next year or two and already have any ideas of prospective advisors you'd like to work with, I'd recommend reaching out to them by email to introduce yourself, tell them why you'd like to work with them, and ask whether they have any idea yet about how they will weight this when considering applicants. This has a few advantage:
Depending on the field and program you're entering, acceptance into graduate programs can be much more a matter of an individual professor deciding to take you on as their student than any formal institutional views.
As such, you should absolutely be getting in touch with potential advisors before applying anyway--many professors don't even consider students who haven't reached out in advance before submitting an application.
It's never too early to get in touch, and showing that you're considering this well in advance and are eager enough to work with someone that you're reaching out to them now will reflect well and increase the chances that they'll consider your application more favorably (assuming it's solid) once you do apply.
If you don't know who you'd like to work with but have any ideas about schools you're interested in, you can also email their graduate advisor or dean of grad studies or whatever the person in that role is called there (although again, depending on the field and your career goals, you might want to pay more attention to individual advisors than schools).
With all the above as a disclaimer that the impacts of a P/NP grade will be highly variable and depend on individual schools and advisors... I'll also just say that many, MANY schools are now switching to P/NP options, so you will be far from alone in having a P or two on your transcript from this semester. I have a feeling most professors won't have much choice but to allow for this unless they want to discount pretty much all their applicants for the next few years. Also, to be blunt, an advisor/program that penalizes you for struggling or choosing your mental health over your grades this semester is probably an advisor/program to avoid. Especially if you're saying that a B would bring your GPA down, you can do better than that.
Finally, I don't know your school's specific policy, but many are allowing you to switch from letter grades to P/NP right up until the end of the semester. So you might be able to wait and reevaluate your options after seeing how your grade is doing closer to the deadline. Good luck!