Seriously, all of these things are massive. Just looking at them gives me carpal tunnel. Nobody needs phones this big. I certainly don't. In fact, I want a very small phone, relatively speaking. The size what we had before we apparently learned better, and there doesn't seem to be many convincing options.
Ideally, my perfect smartphone went extinct with 3.5" displays. I do like reaching the All of the screen without contorting my thumb like some kind of mathematical instrument. I know modern OSes try to work around this by letting you slide or squish stuff around but i don't care. This is a regression, a fix that never needed a problem!
Ironically, Apple's iPhone SE seems to be the closest modern technology I can muster to those halcyon days sans deformed digits at a comfortable 4.7", but those .2 imperial nonsenses do matter, slightly, and regardless I am not keen on Apple's ecosystem. My wife has one of these and I kind of love it anyway. Android at least ought to have some options...? Well, sort of. I have done some digging ahd found a few models that might be OK. I know small beggars can't exactly be big choosers but I am determined to find my glass slippers, damn it.
Cubot Mini/Pocket:
Oh shit. This is perfect! A 4" screen, be still my heart...! However, I am led to believe this entire line of phones won't work in burgerland because this country hates everyone and everything. What?! 
Unihertz Jelly Star:
Love the enthusiasm, but maybe this is a bit too far in the other direction... also, this thing is just kind of ugly. I do have a fondness for that y2k transparency; maybe if it were in a few other colors, but I just can't get into it.
Palm Smartphone:
I genuinely had no idea Palm was still making phones. This actually might be the queen of the crop; 3.3" and from what I can tell, it fits my use case quite well.
And...that's basically it. Everything else that exists won't function with US carriers, near as I can tell. Am I just being a smartphone boomer? I can't be the only one who wants flagship specs on sensible real estate... 
I yearn for a smaller phone too, but I'm Android only and not open to outdated phones + super low budget. :(
If the issue w/ older phones is software you can always use LineageOS! I'm running it on a Pixel 4a and it's a pretty good experience, minus a few quirks
That's useless to me, because
LineageOS isn't Linux based, it's an Android OS.
It's still released for limited phone models and search engine tells me NFC doesn't work on it without workarounds and then maybe it still doesn't. I need a working phone, not an experiment.
That's fair. I myself haven't tried magisk to get around safety net/play integrity because it's not a huge priority for me. I've learned to live without it, but if it's a must for you then I understand.
I'd push back on the "limited phone models" though. Yes, LineageOS doesn't cover every phone under the sun, but for those it does the support is rock solid. The original Google pixel from 2016 is still getting the latest version with all the security update. There should be more than enough variety in the supported devices to find something for everyone.
I recently had to do this with a phone I'd rooted a year or two ago. It only took like 20 minutes. Honestly it's not so bad, if you accept that your banking & streaming apps might stop working like once a year and you have to look up the new fix.
You can also keep an old phone as a backup for such cases. I just used an old phone for streaming for like a week when I was too lazy to fix the safety net check.
Seems to be that NFC/tap to pay works with LineageOS if you have a locked bootloader and gapps. LineageOS is definitely a "working phone" OS (the "experimental" days of Android OSes is like eight years ago, to be honest), but like any non-OEM OS it's going to be a little more involved than just buying a phone at the store
Relocking the bootloader is really not recommend on LineageOS and can result in a permanently bricked device. DivestOS supports relocking but that's a whole different beast with its own compromises.
I believe the pixel 4a has NFC.
It's not issue with phone, issues is with OS not supporting it.
Or postmarketOS if you don't mind a little torture haha
I am not totally sure how outdated the stuff like the above are... the Jelly series says the Star is Android 13, at $200, and then down at around $150 is 12 and 11. The Palm phone is definitely out of the question, I looked at it and Android 8 is pretty outdated at this point I think.
If I buy a new phone I want the newest Android so it lasts.