The new GPU should work well with the existing hardware: but manage your expectations depending on game title. Triple A games will benefit from the RTX3060 and allow you to enjoy the lush graphical environments they're known for but online "battle arena" style FPS titles that rely on extremely high frame rates to get an edge may not since they are mostly limited by CPU performance.
That 2600 is seriously outclassed today. Luckily, a good upgrade into the same motherboard would be a 5600X3d. It's also a good pairing with your new GPU.