Richard Carrier has talked about this, about how emperors before Constantine tried their hand at imposing a religion to unite the empire and to put their stamp on it. Also, there's Ehrman's book on the rise of early Christianity.

I could read Caesar's Messiah, but I don't view these details as being so important. Unless there's a smoking gun, the slim evidence that's available will be explainable in different ways. There are some rational guardrails to help historians pick a model in a responsible way, but much of it seems to come down to personal character, taste, political orientation, and the like.

The two models here are that Rome created Christianity for political reasons, and that Hellenistic Jews created Christianity to make Judaism tolerable to pagan sensibilities. You can see how each model can accommodate evidence of Roman themes in early Christianity. The former model is more conspiratorial, which means its burden of proof might be higher, and if there were a smoking gun in its favour, it would indeed make for massive embarrassment for Christians. The models merge, in any case, once Constantine embraced Christianity and did indeed impose it.

Also, I saw Carrier debate Valliant on YouTube, and Valliant seemed quite hostile and defensive.