> I believe Jesus also believed this
Jesus predicted his death several times, most explicitly in Matthew 20:17–19.
> Now Jesus, going up to Jerusalem, took the twelve disciples aside on the road and said to them, “Behold, we are going up to Jerusalem, and the Son of Man will be betrayed to the chief priests and to the scribes; and they will condemn Him to death, and deliver Him to the Gentiles to mock and to scourge and to crucify. And the third day He will rise again.”
- Matthew 20:17–19
It is known that the specifics of the story were modified.
The current text is kind of frozen by its own similarities to itself.
The use of extracted quotes is probably a mistake. You have to find the same event in a lot of other books beyond Matthew to be able to find a tiny whiff of historical information, very faint, very difficult to do with translated versions.