Quoth https://www.nejm.org/doi/full/10.1056/NEJMcp2306778, A search turned up a lot. Has anyone had a good experience with one of them? I lack a ‘smart’phone, presume some work with a computer

I have no personal experience with them (at least, not yet), but a web search for "online hearing tests evaluated" will turn up a number of articles and reviews from reputable organizations.

And, yes, it seems some do work with a computer. A headset of some type seems to be required.

I asked for personal experiences.
As I stated in my post, I searched the web.

For the test to be even remotely relevant, you'd have to have first properly calibrated your headset and, in the context of your audio card, your system. Different equipment can produce a whole different quality of sound. What will be audible on one system or headset will be inaudible on another.

Then you'd also have to meet minimal specs for a sound proof room or cabinet in which to take the tests. Ambient noise matters.

What's the real goal?

While everything that was mentioned (and not quoted) is of some concern the final, quoted sentence is by far thee most important. I've worked in electronics and music most of my almost 78 years, in studio, in sound reinforcement, live onstage and musical instrument amplifier as well as reproduction gear repair, modification, design and manufacture. I have used several hearing tests online combined with my own evaluations of my listening systems and environments. For a long time I thought I'd somehow escaped hearing damage from playing and listening to music well above 110db. It turned out it wasn't particularly severe but I'm not unscathed and I didn't know that for certain until I took the tests.

Regarding the "real goal(s)", I had mostly 2 different ones. 1) I wanted to test my hearing totally isolated, and 2) I wanted to test my hearing in my most common listening environment.

For #1 I used 2 different sets of headphones, 1 Sennheiser closed cup, and 1 HiFiMan open cup powered by an Asus Essence II sound card running through a Denon DRA-800H, all employing a custom low latency, realtime kernel and with Pulseaudio disbled. I downloaded the test files to mitigate network latency. From averaging multiple tests with each different set of headphones I got what I wanted, a decent overall view of my hearing acuity and discovered I had something of a band reject notch in my hearing between roughly 750Hz and 1.7KHz despite that I can still hear out to well into the 16KHz range (which was part of why I assumed I was luckily unscathed).

For #2 I passed pink noise both directly into my Denon and also via a Focusrite Mic-to-USB mixer into my soundcard to test my speakers with a 1/3 octave spectrum analyzer in my listening area and mapped out the peaks and dips of which there were some but few and mostly less than plus or minus 5db and fairly gradual in slope and bandwidth, not spike-y. From #2 I learned ambient was a far greater factor than I'd imagined since I've apparently grown accustomed to my window fan noise but they have a considerable impact on any results. This test told me only a little about my ears and brain but quite a lot about my in air sound system. This is important to me as I only enjoy headphones as a reference point. I prefer hearing loudspeakers in a room environment.

My overriding goal was to teach myself caution in music editing and production so that I avoiding over boosting frequencies I am less sensitive in and aid me in arriving at a mix that will sound great on top notch audio systems and reasonable even on phones. I can't name any one test that stands head and shoulders above the rest but simply note that results vary and that I think averaging out several is more useful, depending as turbocapitalist and I have said, on your specific goal(s).

For similar reasons, I once went to a clinic (in Nashville) and had a professional hearing test. (Uh huh. In Nashville they do this a lot ...) They declared my hearing overall to be excellent, but pointed out certain frequency ranges which were comparatively deficient. Which is precisely what I needed to know. The entire process took less than one hour and didn't cost much. (I paid out-of-pocket for convenience, and since it wasn't "medically necessary.")

If you are seriously needing to know details about your present hearing capability, as @enorbet apparently does, then I recommend that you do the same. Start by calling local companies who sell hearing aids, and ask them for the names of local practitioners. "They've got the tools, and they've got the talent." (Ghostbusters) You don't need to "guess."