Did Wormtail ever actually buy into Voldemort's agenda or was he just a coward?

We all know that the reasons for which Wormtail betrayed Potters were likely due to his own cowardice. He thought Voldemort would win and chose to be on the winning side, gaining his access by giving up the Potters...or something like that, right?

I also understand why he made the spectacle with Sirius and got him arrested - Sirius was the one who knew and would hunt him down given the chance.

But after being forced out of hiding with the Weasleys, why did he go to help Voldemort?

He escaped and could see quickly that Sirius was nowhere near to being proclaimed innocent. The public didn't know the truth.

Why didn't he simply remain in hiding? He was considered dead, no one would really be looking for him.

So why did he go to Voldemort? Wortmail was instrumental for his return. Did he actually want that, if him joining the Dark Side (lol) was actually just out of fear? Was he scared that if Voldemort eventually returned he would be punished? Did anyone in Voldemort's side know he was even alive?

He seemed to be scared shitless of Voldemort the whole time, he seemed pretty unwilling participant (I know he was willing, but he obviously wasn't vibing with the whole Death Eater society) and he did kind-of-betray him at the end by letting Harry escape.

So did he ever actually believe in Voldemort's cause? If not, why did he come back to him?