I think an excellent question, but perhaps needs to be more specific. - You need to differentiate is ‘what is being judged’, because this makes a difference, it makes the difference - that is, the answer as to ‘Does Jesus Judge’ .... will differ!
Let’s look a little closer ...
The first point to note is seen here.
JOHN 5:22 Furthermore, the Father judges no one, but has assigned all judgment to the Son
The point being that ALL (any) judgement has been handed over to Jesus. A key point! God does not judge man. (This may provoke hermeneutic scrutiny?)
But now we have a issue (for some), because...
JOHN 8:15 You judge according to the flesh; I judge no one.
Now we need precision. This quote from Jesus in context was over an issue over the Law. More about this later ...
Let’s look closer ...
2 COR 5:10 For we must all appear before the judgment seat of Christ, so that each one may receive compensation for his deeds done through the body, in accordance with what he has done, whether good or bad.
This is what theologians call the Bema seat judgement. What is being judged? Works. That is, what you ‘did’ in/with your ‘body’. It’s for ‘reward’, and the standard used in the judgement is righteousness - doing the ‘right thing’.
However, the important distinction to make here is that this is not about salvation, nor ‘sin’. The following verses make this abundantly clear.
1 COR 3:13 each one’s work will become clear; for the Day will declare it, because it will be revealed by fire; and the fire will test each one’s work, of what sort it is.
14 If anyone’s work which he has built on it endures, he will receive a reward.
15 If anyone’s work is burned, he will suffer loss; but he himself will be saved, yet so as through fire.
So here, Jesus does judge. No argument. BUT we need to see that Jesus is judging Works, not ‘man’. This is crucial to note. So, we have this - Jesus judges mans ‘work’, the measure used to assess this the work is ‘righteousness’ - but he does not judge ‘man’.
Now this distinction becomes important when we look at Jesus judging ‘evil’, as in the bowl judgements in Revelation. Obviously judging ‘evil’ is a foundation for much theology, and is outside of what is being answered here, but if you study this, you really need to look at the meaning of ‘evil’ from a Hebraic perspective - very revealing! Nevertheless, let’s move onto what may be the heart of this discussion, or at the least in the back of many minds.
Judging sin. What ‘role’ does Jesus take here. Now this is actually simple, but also very difficult, due to foundational doctrinal views. To judge ‘sin’, you need (the) Law. So, who needs the Law, the judge. And, the judge will condemn the guilty party.
But, does Jesus judge?
JOHN 5:45 Do not think that I shall accuse you to the Father; there is one who accuses you—Moses, in whom you trust.
Here Jesus is saying that Moses judges. Now, we need to appreciate that the reference to ‘Moses’ here means ‘the Law’. It’s a term used for ‘Torah’. So the judge here is the Law. Now, back to our previous verse. ...
JOHN 8:15 You judge according to the flesh; I judge no one.
The context here was the lady caught in Adultery. And, the Law was being used. But, who was judging? Who was using the Law?
Back to your query, does Jesus judge. Yes, Jesus judges righteousness, as part of his reigning righteously. And through this righteous reign, he [will] judges evil. But, Jesus does not judge man..
‘Judging’ is required in or for differing situations - and, it’s the situation that determines whether Jesus ‘judges’. Sometimes the answer is ‘yes’, and sometimes ‘no’ - and only a loose reading or understanding will see contraction.