The OP's question about the two significant events at the last supper teach something about how Satan "does" temptation so successfully.

In John 13:2 we learn that at the last supper, Judas had already suggested to Judas that he should betray Jesus. Indeed, he had already made significant preparations for this, such as a meeting and an agreement with the priests a few days earlier. However, and this is significant, he had not yet actually "done the deed" of betrayal.

[Note the Hebraism: "put into the heart of Judas" is idiom for "suggested to the mind of Judas", or, "put the idea in Judas' mind", or equivalent.]

Knowing humans as well as we all do, it is quite probable that Satan would have been unsuccessful in tempting Judas to betray Jesus in a single step. Instead, Judas was lead down a more gradual path of such great sin, in smaller steps. While each step led him closer, he still had not committed the great sin.

Having taken all the preparatory steps, both organizationally and psychologically, Judas was now fully prepared for the final act of treachery. In John 13:27 we finally learn that he opened his heart and allowed Satan to enter it and take control:

After this, Satan then entered him. ...

Commenting on this Ellicott says:

(27) And after the sop Satan entered into him.—The Greek expresses more vividly the very moment when the mind finally cast out love, and left itself as a possession for Satan. “And after the sop, then Satan entered into him.” It was at that moment, when the last effort had been tried, and tried in vain, when the heart hardened itself to receive from Jesus the sacred pledge of love, while it was plotting in black hatred how to betray Him; it was then that hope took her flight from a realm of gloom where she could no longer dwell, and light ceased to shine in a darkness that would not comprehend it.

Thus, the sad story of Judas and his steady progression from suggested sin to full-blown treachery is documented vividly. We see the distinction between a suggested sin and the act of committing the sin.

This is summarized by the Cambridge commentary:

27. Satan entered into him Literally, at that moment Satan entered into him. At first Satan made suggestions to him (John 13:2) and Judas listened to them; now Satan takes full possession of him. Desire had conceived and brought forth sin, and the sin full grown had engendered death (James 1:15). Satan is mentioned here only in S. John.

The OP's question about the two significant events at the last supper teach something about how Satan "does" temptation so successfully.

In John 13:2 we learn that at the last supper, Satan had already suggested to Judas that he should betray Jesus. Indeed, he had already made significant preparations for this, such as a meeting and an agreement with the priests a few days earlier. However, and this is significant, he had not yet actually "done the deed" of betrayal.

[Note the Hebraism: "put into the heart of Judas" is idiom for "suggested to the mind of Judas", or, "put the idea in Judas' mind", or equivalent.]

Knowing humans as well as we all do, it is quite probable that Satan would have been unsuccessful in tempting Judas to betray Jesus in a single step. Instead, Judas was lead down a more gradual path of such great sin, in smaller steps. While each step led him closer, he still had not committed the great sin.

Having taken all the preparatory steps, both organizationally and psychologically, Judas was now fully prepared for the final act of treachery. In John 13:27 we finally learn that he opened his heart and allowed Satan to enter it and take control:

After this, Satan then entered him. ...

Commenting on this Ellicott says:

(27) And after the sop Satan entered into him.—The Greek expresses more vividly the very moment when the mind finally cast out love, and left itself as a possession for Satan. “And after the sop, then Satan entered into him.” It was at that moment, when the last effort had been tried, and tried in vain, when the heart hardened itself to receive from Jesus the sacred pledge of love, while it was plotting in black hatred how to betray Him; it was then that hope took her flight from a realm of gloom where she could no longer dwell, and light ceased to shine in a darkness that would not comprehend it.

Thus, the sad story of Judas and his steady progression from suggested sin to full-blown treachery is documented vividly. We see the distinction between a suggested sin and the act of committing the sin.

This is summarized by the Cambridge commentary:

27. Satan entered into him Literally, at that moment Satan entered into him. At first Satan made suggestions to him (John 13:2) and Judas listened to them; now Satan takes full possession of him. Desire had conceived and brought forth sin, and the sin full grown had engendered death (James 1:15). Satan is mentioned here only in S. John.