A lot of interesting effort can go into working out how the four Gospel accounts can be harmonized. I find that presupposition determines the outcomes. If you hold that they are traditions cobbled together, then there is no continuity. If you hold that they are the world of God, you can work out a harmony. (“Opening the Gospel of John”, Comfort and Hawley, P. 311-312 is one example.)
My presupposition is that they each have something to say. What is included and excluded fits the purpose of the author, which is not a scientific chronology but a way to present the news.
John lines up, four stories of believing.
Mary Magdalene finds the empty tomb but does not believe, yet. Peter and John run to the tomb, but only John believes when he sees that the body is gone, and Peter does not yet. Later Mary Magdalene meets the Lord in the garden and believes. Jesus appears to the remaining disciples, including Peter but minus Thomas, and they believe and rejoice. Thomas refuses to believe on their testimony, and then the Lord appears to him and Thomas believes.
- John believes based on the grave-clothes in the empty tomb.
- Mary Magdalene believes based on meeting the Lord.
- The Disciples (including Peter) believe when they see the Lord and receive a renewal of their calling
- Thomas believes when he sees and touches the Lord.
Then the question is put to the reader in verses 29-31. Jesus said to Thomas that those who believe without seeing and touching will be blessed. John tells us that much else could be written, but this Gospel was written so that the readers (and you the reader) might believe and receive eternal life.
John here is tying up his theme of belief in Christ which leads to eternal life. This is, it seems to me, the main line of argument from chapter 1 to 20. John focuses on just Mary at the Tomb (though the “we” of v. 2 suggests others were there.) He highlights John and Thomas as well. His purpose is to present 4 individuals who believe: Mary, John, Peter (with the disciples) and Thomas. Each has a unique story. Then he turns to the reader or hearer of the Gospel and says, in effect,
“What about you?”