> They will perceive your lack of response as you not prioritising them.

And correctly so: you are prioritizing people that contact you in the normal way (via phone calls).

If I send you a text message, it's usually because I don't need an immediate reply; answering me tomorrow is good enough. If I do need a faster reply (if I'm texting an image or some such, or in a noisy place), I'll make a call afterwards, just long enough to set off your ringer so you hear it.

I also deal with notifications in a different manner: I have different ringtones and extensive notification filters set up. Most of my apps will not make any noise with a notification while the screen is off. Most notifications will not show up on the lockscreen. Most notifications will not show up in the status bar. My standard ringtone is an mp3 with a short quiet ring and a long pause before it ends, so while I do get call notifications they're easy to ignore; only important contacts (family) are allowed to bubble or pop on top, and they also get a different ringtone.

I dread migrating my phone, as none of this can be backed up. I changed phones last year and still find the occasional app that I forgot to blacklist notifications for and never noticed because things related to https://dontkillmyapp.com simply prevents it from running altogether when I haven't used it in the past couple days.