This post didn't lead to me discovering any new devices, and I haven't heard from anyone who found something they valued via it. So overall not a success, but it was easy to write so I don't regret the attempt. 

You likely know this already, but future readers might not: There are a couple potential gotchas about using pulse oximetry on its own to rule out a trip to urgent care. Both are edge cases of the fact that it's actually measuring the ratio of bound to unbound hemoglobin in the blood as a proxy for blood oxygenation. Both can be pretty confidently ruled out by an additional gadget.

First, carbon monoxide binds to hemoglobin even more readily than oxygen does. Someone who's been breathing CO may read 100% on a pulse oximeter, because 100% of their hemoglobin is bound to something, but it's bound to CO instead of O2 so they're not getting properly oxygenated. This can be addressed by having working carbon monoxide detectors in your home.

Second, if there's not enough hemoglobin going around your system due to internal bleeding, you can have 100% of the available hemoglobin bound to oxygen and yet not be getting enough total number of oxygen molecules delivered to your body in the time frame that the tissues need it. This edge case can be addressed by monitoring your blood pressure, as it'll often (but not always, at first!) change as your body tries to compensate for blood loss. Monitoring for any signs of GI bleeding or unusual bruising can also help make sure you seek care at an appropriate time even if the pulse oximeter reads 100% saturation.

Those are the major situations in which a pulse oximeter will claim you're OK when you actually aren't. When you're confident that you've got an appropriate amount of hemoglobin going around in your blood and there's no CO in your environment for it to bind to instead of oxygen, the device will be a pretty accurate proxy for whether your breathing is adequately oxygenating your blood.

Edited to add -- there's another gadget that someone who cares a lot about measuring their respiration might want to know exists, and it looks like they're available for a couple hundred bucks for home use. It's called an end-tidal CO2, or etco2, monitor. I don't have the training/background to explain that like pulse oximetry, but it could be good to look into if you often find yourself in the situation of "breathing feels different from usual, I wonder what changed" and enjoy data.

Non-health measurement device recommendation:

We finally replaced our phone & Internet setup of <Wi-Fi router + modem + wireless phone base station> with a single all-in-one AVM router (Fritz!Box), and if I'd known how good such devices are, I would've bought them a decade earlier. Not only does this remove so many interfaces and cables and power adapters and points of failure, it also gives you all the diagnostic features in one device, which makes it much much easier to resolve problems yourself.

Before, any problem with our Internet connection was incredibly frustrating to diagnose because it might be caused by the router, or the modem (neither of which, incidentally, had good logging or diagnostic capabilities), or the cable from the Internet providor to the modem, or the connection between router and modem, etc. etc.

Now, that stuff is all in one device, and diagnostics is so much easier: if I can't login to the router from any of my devices, it must be a problem with the router. And if I can reach the router, I can run the comprehensive on-device diagnostic tools, which can in turn tell me where the problem is and even what to do about it.

I second the section on air quality monitors. I only have a CO2 monitor, but find it really helpful for problems of the form "I feel vaguely KO. I wonder why that is... <consults CO2 monitor> Oh, I should've aired the room out hours ago.".

Some additional notes on this topic: The monitor I have isn't particularly good for this purpose. It was a test winner from Stiftung Warentest (the German customer review site), so maybe it's particularly accurate, and I certainly paid as if it was. But it turns out you just don't need a particularly accurate device for this purpose; it's enough if the displayed values are sufficiently correlated with the actual ones. A cheaper device would have been just fine.

Furthermore, to maintain this (supposed) accuracy, the monitor has a truly ludicous design: Any time it's disconnected and reconnected, like when it's installed in a new room, it re-calibrates itself under the assumption that the room has just been aired out completely, and assumes that the current CO2 level is 400 ppm. Afterwards, it re-calibrates itself such that it assumes the lowest CO2 level in the last week was 400 pm. These two aspects make it utterly useless for measuring CO2 anywhere you can't air out completely, like a cellar. (Though it's fine in my room, which I air out regularly.)

In a second feature, the monitor has an optional CO2 alarm and begins beeping when the CO2 level reaches a set threshold like 1500-2000 ppm. Unfortunately, its CO2 measurements take a while, so when it beeps you either have to manually turn off the alarm each time (there's no snooze button), or air out the room for 20+s before it stops.

In conclusion: monitors for CO2 or air quality yay, this device nay.

Watchband and ring fitness trackers will sometimes claim to report HRV, but they're not very good. Measuring HRV requires very precise measurements, and the signal of the heartbeat gets fuzzier the further you are from the heart. When I look next I'll be looking for something favored by HIIT nerdjocks, because HIIT also requires very sensitive measurements.

Health trackers vary a lot in quality, so it might be worthwhile to briefly check the Quantified Scientist Youtube channel (or even email him) for whether he has found any he could recommend for that purpose. I really like that channel for doing calibrated tracker measurements. Imagine a world where those kinds of product reviews were industry standard, instead of SEO content mills.

As a gardener, a simple rain meter like this one has been a useful tool I found in recent years. AcuRite 5" Capacity Easy-to-Read Magnifying Acrylic, Blue (00850A2) Rain Gauge https://a.co/d/iRd0phK

Weather forecasts will often predict how many inches of rain are probably coming, but it's surprisingly hard to find records after the fact of how much rain actually fell. So you might not know, especially if the rain falls at night or when you're out of the house.

Knowing whether we got 0.1 inches or 1 inch of rain can make a difference in my watering plans.

A soil moisture meter probe can also be useful, but usually I don't think about using it, so it hasn't done much for me personally other than calibrating my instincts the few times I did use one. I would recommend one for gardeners with less experience or less willingness to kill plants than I have.

A USB microscope. Just point it at an arbitrary thing and learn more about it! (Say "Examine" for good luck.)

I don't have the following, but I wish I did: A heat camera, an ultrasound probe, a sound camera, an e-nose. Sensors ought to have high bandwidth, in order to give you a chance to notice any anomalies.

Home water testing: these are periodic tests rather than continuous monitors, and aren't cheap either. My doctor recommended this one but it's more expensive than the water filter I use, so maybe find a cheaper one or skip straight to filtering (the test did verify my filter worked, and this was pretty late in the filter's lifecycle). You can also use EWG to check your city's water data, although it will miss problems in your own pipes.

Did you have a reason to suspect that your tap water in particular was bad (e.g. after seeing EWG's measurements), or was the filtration more of an attempt to reduce all the possible environmental contaminants in general? I have heard a lot about air quality impacting health, but not as much about water quality. I would be grateful to hear about any resources you have in mind for why one should pay more attention to water quality.

I'm curious whether you've used any pain measuring devices. Personally, I'd like something which makes recording pain for a headache diary easier. And is cheap. This review suggests they're all quite expensive, and include more features than is really needed. 

You could look at https://www.hrv4training.com/ to measure your heart rate variability. I believe it uses your phone camera and is scientifically validated. Should be more affordable.