So it's a common trope that beliefs give gods power, but I don't actually think that's how it works. In significant part, "power" doesn't seem like a useful way to phrase what gods do in the first place.

What I do think is that belief helps give gods *form*. How a particular god manifests and expresses themself is due in part to what folks expect of them. It's bidirectional, since a god does tell followers some about who they are. The manifestation is negotiated.

This is a big part of how gods (hopefully) adapt to changing cultural contexts. As time changes, a god can adapt their nature while still retaining their identity.

Also I *think* structured belief can accrete new gods out of unformed god-stuff but that's something I'm less sure about, and would probably irritate some hard polytheists.