I see the problem. Imagine drawing a line extending your forearm bones past your hands. That line
should land on the bars or hoods to carry your upper-body weight. On your bike, the line is aimed outside of the hoods and all the weight goes into the soft flesh at the base of your thumb. You want to bend your wrist and rotate your palms inward so that the weight is on the heel of your palms instead of on the thumb. There can be multiple causes of numbness, but I think in your case, it's primarily with how you position your hands:
1. HANDLEBAR HEIGHT - the lower the bars, the more weight you'll have on your arms and hands. Also too short of a reach will also tend to have your arms be vertical with the bars too low, your elbows will be locked and all road shock will pound your hands, arms and shoulders with every road irregularity. I prefer to ride with no lower than a 2" handlebar drop and recreational riders might want to have their bars even with the seat.
2. HAND-POSITION & GRIP probably makes a significant contribution as well. Don't grip the bars so tight! Gripping the hoods/bars tight is compensation for unbalanced positioning. The weight-bearing spot on your hand should be on the heel of the palm:
To really find this spot, do some push-ups and hold yourself up. Notice where the weight is... note that you do not have to grip the carpet to prevent yourself from falling over. Note that you can wiggle all your fingers. The weight-bearing spot is on an imaginary point directly where the forearm bones would extend through your palm.
Now on the bike, place your palm on the bars/hoods so that this spot is directly centered inline with the forearm bones. This spot is not directly over the bars, but rather 45-degrees behind it so that from the perspective of your shoulders looking through your arm-bones, the bars are inline with the bones.
Good way to test is this to release all your fingers, all your weight should be passively supported by the heel of the palm. If you slide off the back of the bars, move your hands up and forward a bit. If you slide off the front of the bars, move your hands back a bit. Finding this perfectly balanced spot will allow you to ride with all fingers loose, try wiggling them all at once. Like this:
Another variation on this is to curl in the fingers and resting the nails on top of the bar.
Couple different ways to rest on the hoods:
You can lightly wrap the fingers over the tops of the hoods or around the side, but no gripping necessary if all your weight is on the heel of the palm. You should be able to freely wiggle ALL your fingers, including the thumb.
With no muscles clamping with a death-grip on the bars or hoods, your hands will get more circulation and they'll feel more comfortable. With your hands on the drops, you want them splayed out about 45-degrees like that last photo so that all of the weight is on the outside heel of the palm.
One thing you want to be careful about is positioning your weight in the valley in the middle of the heel. The median nerve and flexor tendons runs through there and putting weight on it will pinch and cause numbness and pain. I can ride a hundred miles with bare handlebars and no gloves without any problems. It's just a matter of balancing your weight on parts of your hands that's tough and avoid the tender spots. Here's some other riders with their hands positioned for no-pain riding (notice the bent wrist and forearm bones aimed at the hoods or bar):
