OLEDs look very nice. Even older games look amazing on it, especially with auto HDR. If you have a store like Best Buy or even Walmart nearby, go look at the demo models. It's a pretty significant difference. Also most computers can run two monitors simultaneously so you can keep your old monitor and two monitors is really nice for doing any sort of work, even hobby stuff.
OLEDs are more expensive though. As far as burn in, I've had an OLED TV which I use as a monitor for several years and haven't had a burn in issue. However, it is still a problem in general. My TV has pixel shifting which moves the image by one pixel imperceptibly, and an auto-dimming feature when an image is static for a while, which help. I also have my screensaver set pretty aggressively.
Unlike other modern screen types, burn in on an OLED is permanent. The only way to "fix" it is to dim all the other pixels to match the burned in image, which reduces the screen's overall brightness. But again, I haven't had an issue and it doesn't seem to be a widespread problem.