If you're looking at Matthew 24, I'd suggest you compare to Luke 21. As you say, keep in mind hte OT language for judgement. Also keep in mind they don't fully understand the nature of the kingdom. Jesus at times answers their questions truthfully without correcting their misunderstanding. It takes some work to sort it out.
In Luke's account, Jesus says the temple will be destroyed (v6), which they likely (falsely) interpreted as the end of the world. They responded with 2 questions in v7
but when will these things be? And what sign will there be when these things are about to take place?
His answer many interpret as describing the end of the world, but I'd suggest He's simply describing the end of Jerusalem & the temple (destroyed around 70 AD). In vs. 34-37 the message is very much: be on guard, pay attention, you will recognize this when it happens. History records the Romans encircled the city, briefly pulled back, the Christians fled the mountains (likely due this passage), then Romans came back and destroyed the city with most of the Jews still there.
With that explanation in mind, Matthew 24 becomes easier to parse.
V2 Jesus says the temple will be destroyed. But in v3 Matthew records 3 questions in response "Tell us, when will these things be? And what will be the sign of Your coming, and of the end of the age?"
They presumably thought they were asking the same question 3 ways, but I'd suggest the last is a very different question. The first 2 are are related to the destruction of Jerusalem ("these things" = temple being destroyed, "Your coming" = coming in judgement, also destruction of Jerusalem). But the end of the age (end of the world) is a very different question even though they likely thought it was all the same thing. Jesus answers the questions without clarifying their mistake.
Up through v35 is dealing with the destruction of Jerusalem (Jesus coming in judgement against the Jews). The tone though that remains "watch for it, be prepared". This loosely aligns with the message in Luke's account.
Then there's a curious shift in tone from v36 onward which I'd summarize as: it won't happen for a long time, people won't recognize it, they'll give up and be surprised when it happens. This fits the end of the world (end of the age) question that Matthew includes, but not luke.
Many denominations will say all of Matthew 24 is about the end of the world / second coming of Christ. But that doesn't fit the message they will reconigze it, and it will happen before they die (v34).
But if you notice the Matthew 24 has 1 extra question compared to Luke 21, it becomes very helpful to notice the common parts of the answers between the two accounts and the extra part of the answer in Matthew. If we assume the extra part of the answer (v36 on) goes with the extra question, the shift in tone (that might otherwise appear contradictory) makes perfect sense.