Get a “cushioned” shoe (nimbus, glycerin, triumph, etc) and use an off the shelf arch support like superfeet.
Many years ago I was an All American collegiate cross country runner with freakishly high arches. I had success with Brooks Gylcerins and green Superfeet. Later in life I used Saucony Triumphs w/ same brand arch support.
Try to get to a proper running store and they will watch you run and look at your feet (for free). They will likely bring out 3-4 different brands of the same type of shoe. Try them all on with the support. This is very important: one of them needs to feel like the single best thing you’ve ever had on your feet. Like the shoe disappears. Buy those.
Ignore the stupid clownish colors of the upper. Running shoes are tools, not fashion. You can use your cycling socks but if your self-conscious about how that looks don’t skimp on proper running socks.
When you’re ready for another pair, don’t go through this same process. Just pull out the support and throw it into a new pair of the exact same shoe.