I tried to find antyhing that will work and its worth the money but it's just hard. Most of the CPUs on socket 1151 lose 15-25% fps in games with rtx 3060, + my knowledge on sockets 1151 isn't good enough to know if they work with other sockets. I just dont wanna mislead you. Im sorry.
I know it's easy to say and its the worst solution but i think you should consider first new MOBO with newer socket, and its not only about cpu socket. RAM slot doesnt support much aswell. From my experience I know very bad thing to buy kinda "newer" things to make them work with your older pc. Espesialy expensive At the end you lose more money.