One curious question is why the Synoptic Gospels have so much to say about demons, in contrast to the paucity of references in the OT, or the rest of the NT.
The short answer is that we don't know the answer. We can only speculate.
i) I suppose the liberal explanation would be evolving belief in demons. However, that's implausible–even on liberal assumptions. Belief in evil spirits is very common in primitive societies.
At best, what would evolve is an explanation for their existence. A backstory. An organizational chart.
Moreover, the evolutionary explanation fails to explain the paucity of references outside the Synoptic Gospels. Take John's Gospel–or Acts.
ii) There's a pattern. Demons are typically mentioned in reference to exorcism. Absent the context of possession and exorcism, there's little occasion, from the viewpoint of Bible writers, to mention demons. That's their basic selection-criterion. The existence and presence of demons is a topic that normally crops up in that particular context.
iii) That's true in extrabiblical Jewish literature, viz. Tobit, Josephus (i.e. Eleazar), the Genesis Apocryphon, Qumran lit. (hymn 11Q5/11QPs-a).
We also have the Jewish exorcists in Acts 19:13-19). That's an incidental witness to the practice. Luke happens to mention that only in connection with Paul's ministry.
So belief in demonic activity was more widespread than the relative silence of Scripture would indicate. The fact that references concentrate in the Synoptic Gospels doesn't mean this is novel or exceptional in the general culture.
iv) I doubt it's incidental that in all three Synoptic Gospels, Christ's encounter with Satan precedes accounts of exorcism. That's the first skirmish in an ongoing series of spiritual battles. Having lost the first round, Satan delegates subsequent engagements to his lieutenants, although he makes a strategic reappearance to recruit Judas.
v) The fallen angels were expelled from God's abode. Now God enters their abode. His presence behind enemy lines, in the person of the Incarnate Son, naturally draws them out of the shadows. He invades their sphere of influence.
This, in turn, generates situations of mutual recognition. Both Jesus and demons are outwardly human. Both Jesus and demons can discern what lies within. Hidden divinity and hidden possession.
vi) Jesus had inherent authority to expel demons. And he authorized his disciples to expel demons. Due to his reputation as a powerful, successful exorcist, many people brought possessed friends or relatives to him (or people they deemed to be possessed), to be delivered.
The reason the OT has so little to say about this may be because, as a rule, OT Jews had no special ability to recognize possession or expel demons. Possession isn't evident unless the demon chooses to manifest itself.
Moreover, there's no presumption that Jews or Christians have specific authority to command demons. That doesn't mean Christians can't perform exorcisms. But there's no guarantee that their efforts will be successful. So we wouldn't expect the same emphasis outside the Gospels.
vii) Likewise, the Gospel has a preemptive effect, by suppressing the occurrence of possession. By driving the dark side back into the shadows.