Will my uncanceled work permit extension affect my long-term visa application in Thailand?

Yes, most likely, you cannot apply for a long-term in-country visa and/or yearly extension at the local immigration office inside Thailand until you cancel your existing extension, regardless of whether it's expired or not.

Go to the immigration office that issued that extension to cancel it next time you are in Thailand. You may also need to cancel your old work permit if it's not cancelled as well. You may or may not be fined (same rate as overstay fine, up to 20K baht) for not cancelling it properly, depending on when your extension based on employment expires.