Warning: As pointed out in comments the speed at which you develop numbness suggests a more serious lurking issue that the change in position may be setting off, it could be worth seeing a doctor as it sounds like you have a lot of inflammation.
so what I want to ask this group is whether there is anyone riding a road/gravel bike with flared drop bars who finds them very comfortable, or if many people here have had similar issues?
I have been using flared bars for about 4-5 years now on my commuter (12 and 16 degrees). I personally find them quite comfortable on my longish commute (~1.5 hr a day). They took some time to adapt to but I found they afforded improved breathing and shoulders position, especially as I also adapted my fit to better suite the bars. Compared to regular drop bars, I find flared bars are more suited to a upright + shorter riding position where you set your shoulders back (similar to standing) open up your chest and flair out your elbows a lot more. I even went with a bar that was 2 cm wider than my more aggressive “fast” road fit, as the flare seemed to suite a more wider overall arm position. All in all, I find the wider more upright position is quite relaxing for long rides and encourages you to support proportional less of your weight with your hands and wrists, compared to a more classical road fit.
I've found that to keep my wrists straight, I have to spread my elbows out ridiculously, otherwise no matter how I hold the bars, I end up with my wrists pointing outward after a few revolutions. I'm trying to decide whether the problem is the flaring and I just need straight drop bars, or whether I'm too close to them and so my wrist bending is inevitable.
The fact you are falling into a pattern of pointing your wrists out, rather than your elbows, is concerning and probably isn't helping the numbness. If anything I would hazard a guess that it is a driver behind your numbness. As you point out in your question flared bars encourage a very wide elbow and arm position, bringing your elbows in means that you need to compromise on your wrist position, which is not ideal for extended periods.
If you do not like, or cannot adapt to having your elbows flared out, then you may need to switch to a regular low flare drop bar. That said, you can also try working on your riding position by focusing on keeping your elbows flared and your wrists in a more neutral position. You may also trying a more of an upright position, as it is more natural to ride with flared out elbows if you are more upright.
Finally, position changes can take time and may not feel "intuitive" at first, especially if you have spent a lot of time in a more classical aggressive road position.