Did the Spirit want Paul to go to Jerusalem in Ac 20-21?

Luke was with Paul in Miletus in Ac 20:

16 For Paul had decided to sail past Ephesus, so that he might not have to spend time in Asia, for he was hastening to be at Jerusalem, if possible, on the day of Pentecost.

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Paul wanted to go to Jerusalem. He arrived at Ephesus:

22 Now, behold, I am going to Jerusalem, constrained by the Spirit,

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Paul felt the Spirit wanted him to travel to Jerusalem. He believed he was following the Spirit's leading.

not knowing what will happen to me there, 23 except that the Holy Spirit testifies to me in every city that imprisonment and afflictions await me.

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He did not know exactly what would happen there, but he knew the Holy Spirit told him to expect harsh treatment from different cities.

25 And now, behold, I know that none of you among whom I have gone about proclaiming the kingdom will see my face again.

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Paul had some inkling of what would happen in Jerusalem.

36 And when he had said these things, he knelt down and prayed with them all. 37 And there was much weeping on the part of all; they embraced Paul and kissed him, 38 being sorrowful most of all because of the word he had spoken, that they would not see his face again. And they accompanied him to the ship.

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They knew bad things would happen to Paul in Jerusalem but didn't advise him not to go.

Paul and Luke arrived at Tyre in Ac 21:

4 And having sought out the disciples, we stayed there for seven days. And through the Spirit they were telling Paul not to go on to Jerusalem.

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The Spirit inspired the brothers at Tyre to tell Paul not to travel to Jerusalem. This was to test Paul's resolve to strengthen his faith and commitment. Paul insisted on moving forward.

Now, did the Spirit inspire Paul to go to Jerusalem?

I think so.

They arrived at Caesarea:

10 While we were staying for many days, a prophet named Agabus came down from Judea. 11 And coming to us, he took Paul’s belt and bound his own feet and hands and said, “Thus says the Holy Spirit, ‘This is how the Jews at Jerusalem will bind the man who owns this belt and deliver him into the hands of the Gentiles.’”

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Agabus quoted the words of the Holy Spirit to warn and prepare Paul.

Did the Spirit inspire Agabus to tell Paul not to go to Jerusalem?

No. The Spirit inspired Agabus to tell Paul what would happen to him in Jerusalem. That didn't surprise Paul; he knew it more or less (v. 23).

12 When we heard this, we and the people there urged him not to go up to Jerusalem.

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Luke and the brothers in Caesarea urged Paul not to go.

Did the Spirit inspire them to urge Paul?

No. They did it out of their personal concern for Paul.

13 Then Paul answered, “What are you doing, weeping and breaking my heart? For I am ready not only to be imprisoned but even to die in Jerusalem for the name of the Lord Jesus.”

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Paul insisted on going despite the hardship waiting for him there.

14 And since he would not be persuaded, we ceased and said, “Let the will of the Lord be done.”

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They resigned to the will of the Lord.

17 When we had come to Jerusalem, the brothers received us gladly.

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The brothers in Jerusalem didn't tell Paul to run away.

Did the Spirit inspire Paul to go to Jerusalem and simultaneously inspire his friends to tell him not to go?

Yes and yes.

Was that contradictory?

No. The Spirit inspired Paul to go. That was Paul's mission from the Spirit. The Spirit inspired his friends to tell Paul not to go because of their personal concern for him and because God wanted to test Paul's resolve through his friends. This dual action allowed Paul to demonstrate his faithful character before the disciples so that they and we could learn from this series of oppositional events.