Need recommendation for CPU upgrade.

You will need an entirely new CPU platform (CPU, motherboard and RAM) in order to continue updating Premiere Pro. You see, your system's current motherboard cannot accept anything newer than your current E5-26xx v2 CPU. (Or put it this way, none of the CPUs that are compatible with your motherboard support AVX2 instructions at all.)

P.S.: New RAM is required for any newer CPU platform because the DDR3 RAM that's currently in your PC is completely incompatible with current CPU platforms. (As in that DDR3 RAM will not even physically fit into, let alone work electrically with, the DIMM slots of any current-gen motherboard.)

In general you want an i7 or i9 with 'many' processors

BUT

What does the motherboard manual say you may use?

If that motherboard will not allow you to use an i7 or i9 you will have to replace the motherboard... and that MAY mean new Ram to fit what the motherboard uses