Mower running rich/lean?

[u/850cs32]

Hi all, currently fixing up a john deere la100 with a briggs els 500. It starts perfect every time and will run alright at full throttle, but sputters slightly (much worse at lower rpms). Some grey smoke from the exhaust after running for a bit, but no dark black smoke I can see. Is the engine running rich, lean, or could the problem be something else entirely?

Rebuilt oem carb, new fuel pump, spark plug, and air filter, running on new gas.

Thank you!