I've never been into anything but riding a road bike with drop bars since my early teen years. So I'm biased in that respect.

However for anything, I'd think in 2 rides that you just haven't gotten used to it yet. And perhaps your wrist and hands are in the wrong position. Now my bias is going to show, I don't think a flat bar will let you put your hands in a decent position. However, other's do it and apparently with success. And I see plenty of people on hybrids with flat bars that ride the 100 mile century rides.

While you are waiting for your body to get used to it, you can play with saddle position both fore and aft of where it's at now, and also play with bar height. For me, a lower bar height helps with weight on the wrists and hands. For others a higher bar helps, but for me that would put more weight on my butt and make it sore on my longer rides.

Tires can make a difference in ride, even in the same size. Typically I've found that puncture resistant tires are the worst. Inexpensive tires with some exceptions are harsh riding too. Probably won't be enough of a difference for what you are experiencing though. However if you are down toward the lighter end of the weight scale, you can get closer to the lower pressure spec'd for your tires.

If you are going to go to the trouble of installing a suspension fork, then consider if you ought to just get another bike with one. Like tires, I don't think it will materially affect your issue. A lot of us ride bikes with no suspension and no wrist problems.

Play with the fit of your bike some more. Assuming you bought one within a couple sizes of ideal, then you should be able to make it work for you. You'll also be surprised how muscles and joints will gripe when you've been off a bike for a seemingly short time.