The crucial point is that Christ was the passover Lamb. He was killed the same day that the animal lamb was being killed (probably at the same time), in preparation for the Passover, since they could not do any work on the passover, it had to be done before.
Thursday crucifixion Friday Passover makes sense. Friday crucifixion does not.
In terms of the high sabbath, it could still work for the passover to be on a Saturday (Friday evening). Christ's death would occur in the afternoon (the "evening" seems to mean while the sun is going down...from its apex that day). But there are other things in play. The requirements for the passover include selecting the lamb (goat kid was ok) on the 10th of the month, and keeping it with the family until the 14th, when the sacrifice was accomplished. I think Jesus' triumphal entry is the selection, and it occurred on Sunday. The 14th would be Thursday. But if they kill the lamb on the 14th, they eat it on the 15th, after sundown of the 14th.
As
@Idolater mentioned, the synoptic gospels indicate that Jesus ate the passover meal on the night before He was killed. One suggestion I've heard to reconcile this is that the Galilee passover ended up one day earlier because of when the new moon was first seen there compared to Jerusalem. Or perhaps they were "beyond the Jordan" at the new moon, something like that. I don't know why Jesus ate "the passover" with His disciples a day earlier than the leaders of Jerusalem ate the passover.
I expect that if we understand the timing correctly, it would pinpoint the correct year of His crucifixion as well.
