Mike Duncan is indeed great, but that’s not really the scope of The Storm Before the Storm. I’ve read it twice, in fact, and the purpose is to show the decline of the Roman government, and especially the internal conflicts that caused said decline, that led to the collapse of the Republic.
To answer your question, griffin1977, we need to distinguish between the oligarchic Senate and the democratic Assemblies. Well, the Assemblies were partly democratic; the Romans never had bodies to represent the abstract “People” but rather different groupings, each with its own history. These all overlapped but didn’t share power, nor was there any concept of “embodying the sovereignty of the nation” like, say, Parliament or Congress. But they could be potentially very powerful; even the Senate couldn’t override them which is why the Gracchi caused such fear.
When Augustus took over, he was very careful to make clear that no one was allowed to rival him, but also to act as a kind of “super-Chancellor” over many of these groups and bodies, or have them controlled in some other way. So he became a permanent Tribune while also wielding official powers as Consul and (effectively) Censor.
The Senate was slowly turned into a tool of the Emperors, but it remained a tool with two edges. By the end of the civil wars, the Senate had been devastated with many deaths, and Augustus, along with some later Emperors, filled it by promoting more reliable Equestrians. This made the body more loyal, at least temporarily, but it seems like every so often a random group of Senators would start some plotting. This could be well-intentioned (we must rid ourselves of this wicked/crazy/incompetent Emperor!) or very ill-intentioned (we must rid ourselves of this obstacle to our ambition). Usually there were elements of both, but the constant scheming made almost every Emperor very leery of trusting the Senate with anything at all.
However, while the Senate became almost irrelevant following the end of the Julio-Claudians, the pretense was kept up for another century. Eventually, however, the fact that the rulers of Rome rarely entered Rome itself sort of made any claim to importance obsolete. Senators didn’t hold important positions, weren’t trusted more than any random provincials, and due to never holding or even wanting military positions were never going to be Emperor. But, there were Senators even though there was no longer a Senate. It remained a kind of cheap way for Emperors to reward important and loyal supporters - with a title.