The verb "plead" has 2 meanings. One meaning is similar to "beg;" She pleaded for leniency, or I pleaded to the principal on my child's behalf. This verb needs an object.

The secondary (less common, legal) meaning is "to make a statement about the facts" Ex: He pled not guilty. The officer pled his ignorance on the matter. Or the fixed expression "He pled the fifth." This is the only sense where "entered a plea of" could be synonymous. This is a stative verb.

For the first meaning, the past form is "pleaded (for / to)." For the secondary (legal) meaning, the past tense form is "pled."

I did legal work for many years in the US, and I currently teach English. This is my informed opinion, and I'm sticking to it - although I really don't care which term people use.