So i believe fredbear plush from fnaf 4 (yes, the one that talks to CC) is actually the puppet, let me explain;

First, theres not enough evidence for him to be william. I agree that william watched cc with the plush, but theres not enough evidence as to william being the one speaking, theres only the cameo the plushie does in sister location, but its not enough evidence.

With that out of the way, i think its actually the puppet possesing the plush because;

1- shes the FIRST to be killed, either in 82 or 83, it doesnt matter, she's the first to posses an animatronic.

2- theres a line in ucn, "im not afraid of you, not anymore", which implies that puppet was afraid of william sometime back, which means that, she could well know about crying child's suffering, and, just like she did with the mci, she wanted to help him, 'lift him into her arms'

3- in the fnaf 2 movie theres the faz talker, which is actually just the puppet using it to lure Abby to where she wants.. so, suspiciously, an possesed item speaking to a frustrated child?... I think its very likely puppet could be possesing the plush