This particular question is of an age-old issue with volumes having been written about it; much, much more than can be practically referenced in an email, and there are tons of stuff on the internet, in journal articles, and even whole books.
From an academic perspective, these questions are but one aspect of what scholars call the "Synoptic Problem" trying to reconcile the Johannine accounts with the Synoptics. It has been the source of liberal higher critics exploiting this issue in their attempts to discredit the historicity of the Gospel narratives being responded to by Conservative Evangelical theologians (such as Dr R.T. France, one of my theology professors and a good friend who is now with Jesus). It has also been ammunition used by certain rabbinic scholars to discredit the reliability of the plausibility of Christian claims as to Jesus being the Promised Jewish Messiah. These have been responded to by Messianic apologists, some of whom I know or have known. This, in short, is a longstanding, (not new), and a much-contested issue that in scholarly terms is a sub-debate of the much larger overall synoptic issue. It is too massive for me to address comprehensively. Linguistics, Source and Form literary criticism, 2nd Temple Period Jewish Sitz im Leben, and more come into play. I will therefore only address the question without any academic jargon and in brief.
There are at least four (possibly five ) standard explanations of this apparent contradiction, and several combinations extrapolated from these. All have some credence and none are devoid of credibility as possibilities. None however is absolutely proven. This does not impact the reliability of the texts, it simply means that there are varied theories for solving the issue.
It is like anything else - a medical diagnosis, a criminal investigation, an archaeological exploration. Each body of evidence can support a conclusion, be it a judicial verdict, a clinical diagnosis, or the comparative analysis of ancient documents. There is common agreement on certain things, but there are usually "loose ends" or "Unconnected dots"; as it were 'a few odd socks'.
Suggested calendrical differences between the Galilean Jews and Judeans, and variations in the Essene and Samaritan calendars, are at most speculative partial solutions.
Just as in a criminal trial a defence lawyer for a guilty client will try to amplify circumstantial evidence out of proportion attempting to convince a jury not to convict despite the prima face evidence being indicative of likely guilt, this unfortunately also transpires in the church (for instance, the New Testament overwhelmingly supports Believer's Baptism - but Anglicans and others highlight nebulous passages on baptism as if they were cardinal passages in an effort to justify infant baptism.
Liberal scholars however are much worse, but play the same game. Those holding to infant baptism are misled by the devil on that one point. Theological liberals (some of them are atheists) however are out to mislead others on behalf of the devil on all or most points. This case of the Paschal accounts in the Gospel Passion Narratives is among their favorite weapons of choice. Of course, their actual hostility to the real Christ is camouflaged in 'academic parlance', but they are the servants of Satan, like him (as we are warned in 2 Corinthians), appearing as 'angels of light'. Note well. These and those who believe them are what you are up against.
Let me preface my own remarks by stating that this is (hopefully) sanctified opinion - I am not being dogmatic. There are other opinions that, as I have already stated, may carry credence as alternative solutions, but too many for me to elaborate on at length.
A comprehensive or exhaustive approach to this subject is something you will need to embark upon for yourself if you wish to.
* We need to begin not with the apparent discrepancy, but with the obvious consistency. All four Gospels agree that Jesus was crucified it was preparation for the Sabbath Preparation (John 19:31, Luke 23:54, Matthew 27: 62, Mark 15:42).
- THIS IS THE PREPARATION FOR THE WEEKLY SABBATH, IT DOES NOT STATE IT WAS THE 'PREPARATION FOR PASSOVER'
The Passover preparation is the 'bedikat hametz' בדיקת חמץ (Search for leaven) and organizing the 'Seder', and these are not referred to in the Gospels as Pachal Preparation. Some have given themselves license to equate the two, but we must NOT confuse the two.
Also note that the abstention and purge of leaven and avoidance of possible contact with it, explains why the Sanhedrin could not enter the Roman Praetorian, as there would have been leaven present resulting in ritual defilement in John 18:28.
THIS DEMONSTRATES THAT THE PASSOVER PREPARATION (BEDECHAT HAMETZ) HAD ALREADY TAKEN PLACE BEFORE THE CRUCIFIXION, THUS THE SABBATH PREPARATION IN JOHN 19:31 COULD NOT POSSIBLY BE THE PRE-SEDER PREPARATION.
* Before the time of Jesus, in the day of Jesus, and in Talmudic Judaism today the entire week-long 'Feast of Unleavened Bread'
(from Leviticus 23:6) was seen as a combined festal observance. It is called Hag Matzot and the week opens with Pesach on the 14th of Nissan. Therefore, at least from the time of Ezekiel 45: 21 (and probably well prior to that), the whole week was called 'Passover' (today it is called 'Passover week in English, but in Hebrew, it is just called Hag Pesach).
*. While the main Seder was for the 14th of Nissan, there were multiple ritual meals. Such an additional sacrificial meal is called a chagigah; there was one primary Seder, but multiple 'Passover meals' (this custom still remains for ultra-orthodox Jews today). This reality should be borne in mind as a possible factor in any related equation. Thus, when we read the Gospel accounts we must understand that in the context, 'Passover' does not merely refer to the first day only.
* Both in Jesus' day (and earlier), and still in Talmudic Judaism today, if a Prescribed Holy Day/ Feast if Israel fell on a Sabbath, it was/is ritually, liturgically, and symbolically of particular note and importance. It is called a 'High Day' (John 19:31). This was the 15th of Nissan (which commenced with Sundown on the 14th and was technically the first day of Passover).
Hence, as John 19:31 and John 19:14 were the same day, the preparation was for the Passover Sabbath (Pesach Shabbat) and the Sanhedrin did not want the high Sabbath to be violated by capital execution.
Therefore, since the Hebrew day begins with Sundown the previous night (based on the Genesis Creation Narrative), the simplest and most straightforward solution is that the Paschal preparation already took place before The Last Supper. Sunset on the calendrical 13th of Nissan was ritually and liturgically the 14th of Nissan.
The Paschal Lamb needed to be sacrificed on the 14th of Nissan but eaten (In the original Hebrew text) 'between the evenings' in NUMBERS 9:2-3. (B'MIDBAR TET: 2-3) the text is clear and unambiguous ('twilight' is not a very accurate translation); the term is:
BEN ARAVIM = "Between The Evenings". God placed this instruction in Numbers 9 for a reason. It allowed Jesus and the Apostles to eat the Seder early, but within the prescribed parameters of time, yet also for Jesus to be crucified in the afternoon (the lambs were sacrificed at 3 PM when Jesus died, but 2 PM if it was a Friday). The last supper lamb would have been killed on the 13th of Nissan, but this did not invalidate the Paschal observance because Jesus Himself would be sacrificed on the 14th of Nissan.
Jesus therefore, with His disciples' could ritually eat the Passover on the 14th of Nissan at the Last Supper, 'between the evenings', and dying for our sins as 'The Lamb of God' the same day the paschal lambs were sacrificed.
I would need to point you to other teachings on Moriel TV and on Moriel.org for Jesus drinking the last paschal cup of completion on the cross (only accepting the wine offered Him the the final time when He said 'It Is Finished' and He fulfilled the Torah and paid the price for our sin in full - John 19:28-30). This further relates to the Passover being eaten in the dark when the prophecy of Amos 8:9 was fulfilled in Luke 23:44). In other words, Jesus observed Passover on the cross in the dark, only with Himself being The Lamb.
But I digress......