Situation:
* Raspberry Pi 4 runs fine with a keyboard, mouse, and hard drive attached to the USB ports.
* Adding a microphone doesn't cause a problem (in my brief test).
* If I instead connect my smartphone, the hard drive disconnects for a bit. Given that the Pi is using the hard drive as its root filesystem, this is a bit of a problem, as now the root filesystem is no longer accessible, no files can be accessed, no commands can be run, and running programs crash when the files aren't there. (At this point, it's necessary to pull the plug.)

Would a powered USB hub help here? Are there other possible solutions?

(Going back to an SD card isn't a good option, as the system will tend to stall a lot, which is rather annoying. I'd rather have the hard drive than be able to charge my phone this way, if I had to choose.)

It could. Pi 4 power consumption is already greater than the consumption of P3, so additional peripherals only increase the demand from power supply. For me standard Smartphone charger was not enough to power standard setup.
https://www.google.com/search?client=firefox-b-d&q=rasperry+pi+power+comnsumption
If Pi is underpowered it also displays warning:
https://www.raspberrypi.org/documentation/configuration/warning-icons.md

Edit:
Maybe asking the quesdtion on Pi forum could be more beneficial

Intuitively, it sounds like it could be a power issue, so a powered hub would be my next step. Alternately, you could just connect your phone to a dedicated charger, if all you're after is just to charge your phone with your computer.

What kind of harddrive and smartphone have you connected?

3A is a little if you plan on connecting several things: power draw on a Raspberry Pi 4 could reach up to about 7.6w (1520mA). Even a 5v SSD can use up to 5-10watts at peak when writing.
https://magpi.raspberrypi.org/articles/raspberry-pi-4-specs-benchmarks

5v * 3A = 15w, which means there is little room here, even with a stable/original source.

The problem might be your phone drawing too much power, which there is little left. I would suggest connecting the phone through a powered USB3 hub, anyway, and test it.

EDIT: SSD is in fact better over the slow SD: https://www.tomshardware.com/news/raspberry-pi-4-ssd-test,39811.html

Phone is a Samsung J3 Star, I believe. Hard Drive appears to be a WD Blue(?) 320GB laptop hard drive (it's originally from a laptop) attached by a USB3-SATA cable.

I can't test with a powered USB3 hub, as I do not own one and do not have access to one.

Oh snap, a mechanical one? Ok, that's even worse when it comes to power draw. :)

At least it's a laptop hard drive and not a desktop one.

(I believe a desktop one outright wouldn't work without external power; this laptop one works fine as long as I don't try to plug in my phone at the same time.)

Edit: Also worth noting that Raspberry Pi OS runs just fine from the hard drive. Boot time might be slightly longer, but only slightly, as the OS was designed for low-spec devices with little RAM (4GB, which may be too small to comfortably run Windows 10 (is Windows 10 IoT better about this?), is a *lot* for a Raspberry Pi, when older models had only 1GB or even half that), and as a result doesn't load a large number of heavy services on boot.

3.5 HDD's won't power from USB alone, it need external power, yes.

I would have gotten a cheap SSD because that 320GB drive is only going to get worse and worse with time. I have two of those same type and I only use them for backup because they are so slow.

Not exactly sure what you mean about the last part there... Load time has mostly to do with the storage it reads data from, not the RAM, so a mechanical drive will be relatively slow anyway(at least compared to an SSD). Beside, when Raspbian (f.ex.) was made for older models, it was written for it, whereas on the RP4 it will naturally load more because it has better capabilities than the older models and it's written for that use.

Personally, I would stay far from 10IoT:
https://www.thewindowsclub.com/windows-10-iot-core-vs-raspbian

I'm very sure that Raspberry Pi OS (what used to be called Raspbian) does indeed load less than Windows and mainstream Linux distributions, so while a mechanical drive is slower than an SSD, it doesn't really *feel* that slow (and, once booted, feels much faster than the SD card did).

When I got the laptop, it had this drive in it. I took it out and replaced it with a 120GB SSD (and put the original drive in the SSD's packaging). Since that laptop has died (display doesn't come on), I could take that SSD out, back up its contents, and use that as the boot drive for the Pi, but I don't feel like doing that at the moment (and it's running just fine as is unless I plug in my phone).

(Another idea is to get a new SSD to replace the one in my desktop, then repurpose the old one after backing up my home directory.)

Edit: Also, load time does have a lot to do with how much stuff is loaded. It's why smaller games can load really fast, while larger games take much longer to load, given the same hardware. (This is assuming the game doesn't have issues like those someone found in Grand Theft Auto 5; even with the two major issues patched, the game still takes 110 seconds to load. Source: https://nee.lv/2021/02/28/How-I-cut-GTA-Online-loading-times-by-70/ )

a ban surely would

Considering most PCs also run into issues if you try to tie 2 or more power hungry devices on the same USB port/hub, a definite yes. A powered hub would most likely allow you to run as many power-hungry devices as you have ports for (assuming the charger is scaled appropriately).

If a powered USB hub will help, the question is, then, *which* powered USB hub should I get?

Interesting, seems they "simplified it" :).

Been a while since I played with my two 3B. Seems I need to play around with retropie/mini nas again... No, really...? O_o

It's hard to make a specific recommendation since it's all just commodity hardware in the end, but if you're trying to diagnose potential USB issues, one possible idea would be to get a USB hub that has switches for each port so you can ensure that the ports you're using are the ones getting power.

There are also USB hubs that have built-in ESD/surge protection to protect against upstream/downstream power surges damaging equipment and devices, but the products I've seen are industrial-grade and very, very expensive.