Been there, done this.
When i started riding some 4+ decades ago I initially rode in shoes like you're using now..that is flexible sole. I used cage (campy) pedals much like you're using now. I rode a lot. My feet were sore after a long day. Eventually I started wearing racing, stiff soled shoes (Sidi) and the feet issues went away. Fast forward many years and occasional foot problems, and my feet are about 75% numb from the front of the arch forward. I think I did some nerve damage by wearing flexy soled shoes. In recent years metatarsal pain has flared up, though I've found a solution that makes it go away.
Do this & your issues will go away.
1) Get some stiff soled biking shoes. Mountain/touring shoes will be fine without cleat ("clipless" SPD cleats). Often you can find pre-owned, like new bike shoes on ebay for peanuts.
2) Get some insoles if you have a high arches (
https://www.amazon.com/gp/product/B0...e?ie=UTF8&th=1)
3) I'm guessing 1 & 2 will solve your issues. If not, get a pair of these
https://www.walmart.com/ip/Strutz-Cu...e&athbdg=L1600
and wear them just back of the metatarsal pads on your feet. Not in your arch, but just behind your metarsal area on the ball of your foot. Google the causes of metatarsal discomfort and you'll understand why this works. Slip them on, wear a sock over them, then put on your riding shoe. It works.
You really need to dump the flexible shoes. Completely inappropriate if you're riding any more than casual, short distances.