Obviously it would be recognizable as a Seder, but I'm wondering if we know of any differences. Also, more broadly, do we know anything of the personal or private spiritual lives of the Second Temple period? Thanks.
To start off with, Jesus lived (obviously) while a temple still existed. That would mean that the Passover meal would consist of the lamb sacrifice. This is today represented by the shankbone on the seder plate, rather than actually being eaten. Additionally, many of the parts of the seder as we know them are rabbinical, rather than biblical. Many stories and songs (Diaynu, the passage about how many plagues there truly were, the four sons, etc.) come from after the destruction of the second temple. A seder in the time of the second temple would be less structured than one is today. No haggadah dates that far back. Rather, seders consisted of traditions that were repeated yearly that eventually evolved over centuries into what we know today, and were, starting in the middle ages, written down so that they could be followed. So, to define it as a "seder"--meaning order--is a bit misleading, since there was no established order at the time.
Edit: Hallel is not made up by the rabbis--thanks GingerKid1234