About 4 years ago, more or less the same time I started needing to wear reading glasses to see up close, I realized I wasn’t able to focus on my front sight.
As you’ve noticed, wearing the readers brought the sight in focus but blurred out the target. On the advice of some friends of similar age I experimented with different strength glasses, and discovered that a diopter strength that was 1/2 my reader’s was a good balance of being able to focus on my front sight and still be able to see my target clearly enough.
For competition shooting, I found a pair of safety glasses in the right diopter strength and use those whenever shooting iron sight guns. But caving to the inevitable, I ultimately made the switch to red dot sights on my comp guns (Carry Optics and PCC in USPSA, RFPO in steel challenge, Open div in 3-gun). I also started adding red dot sights to my carry guns because I realized that I probably wouldn’t be wearing my special safety glasses if I ever had to pull my gun.