> For example, all greek mysteries purported to come from a real teacher, but in most cases these were gods, i.e., not real people.
None of the ancient Greek mystery religions claimed a recent human founder as their central figure. Their central figures were almost all deities, not humans; even when they occasionally centred on a human, it was a hero who lived in the distant uncertain past, not someone who lived at a defined recent historical moment. By contrast, the four canonical Gospels all agree that Jesus was executed while Pontius Pilate was governor of Judaea (between 26/27 and 36/37 CE), and it seems likely those Gospels were composed within a century of that date.
> There is really no evidence of a christian sect forming in Jerusalem at the time of the supposed death of Jesus.
The New Testament is evidence. To be clear, a historical text claiming X is evidence for X. Now, we can argue about how whether it is strong evidence or weak evidence, but either way it is still evidence. And of course, accepting the text as evidence, doesn't mean we have to accept all of its claims as equal in evidential weight, especially those of a miraculous or supernatural nature. If a text makes a mixture of claims, some historically plausible, and others which are (from a purely secular perspective) extraordinarily improbable, it is reasonable to judge its evidential strength as being much higher with respect to the former claims than with respect to the later.
> Christianity appeared for all purposes in the Greek Asian Minor, pushed by someone who called himself Paul, and all the writings we have are from Greek-speaking composers.
The vast majority of scholars accept Galatians as an authentic work of Paul. In Galatians 1-2, he claims the "Jesus Christ" movement which he propagates pre-existed his conversion to it, and he reports visiting its leadership in Jerusalem. So this is evidence that a "Jesus Christ" movement existed in Jerusalem prior to Paul's conversion to it.
> The idea that Christianity goes back to a Jesus and his followers in Judea seems to be a romantic idea used by the real founders of the movement to make it older than it really was.
In order for that to be true, either (1) Galatians is not an authentic letter of Paul, (2) Galatians has been tampered with to insert material claiming Paul visited the pre-existing proto-Christian community at Jerusalem, (3) Paul was lying. While none of that is impossible, it seems less likely than that Paul really did join a pre-existing religious sect headquartered in Jerusalem. In particular, while I'm no expert at biblical Greek, scholars argue that there is no textual evidence in support of (1) or (2).
Saying that Pauline Christianity had its origins in a pre-existing proto-Christian sect headquartered in Jerusalem, is not denying that Paul took it in some innovative theological directions, such that it ended up with significant differences from that starting point. One obvious difference–apparent from Paul's own writings–is a much greater distance from Judaism, moving beyond being a sect of Judaism and towards becoming an entirely distinct religion.