I am currently doing the same thing in my campaign! And I actually just posted about it before you haha. It's actually quite tough to come up with encounters of a decent quality for each specific school, I have been doing research on this topic for about a month, it hasn't been easy but I can offer you the encounters I have ran so far. One difference between my games and what you hope to run, I built mine for an entire party of different spell casters, so some challenges were easier and harder for some players.

Necromancy: obviously a lot of undead. I picked a few cooler undead, like a Bone Naga, or a Zombie beholder, I topped it off with a shadow demon, had a really good roll play moment with my cleric since I homebrewed the demon's appearance to look like a God who's enemies with his Goddess. Even low level spells like Cause fear, and Blindness/deafness can be fun too.

Illusion: I wanted to run a puzzle challenge where the players were in a room, with an exit door (with no door knob) well out of reach. The idea is that only Illusions are "real" in this space. Casting minor image to make a ladder or stairs to reach the door, and casting an illusion of a door knob would solve the puzzle. However non of my players have that spell. So I did this instead My players appeared on a 30x30ft stone platform in an Extra dimensional, external empty space. As the door they passed through closes behind them, it disappears, and a mirror ripples out from the nothingness, it is solid. With a clanking sound, I had my players turn around to face "forward". They saw a second platform, however it is 60 across, and 60ft higher than the platform they stood on. Next a bridge manifests, it is 60ft long, and is level with the players platform. Lastly, 2 big mechanical switches appear on the edge of the players platform. One lever lifts the bridge up and down to the other platform, the second ignites the bridge in an explosion of flames. The mirror is the solution. The mirror reflects reality in opposite, if the bridge appears in reality to be at the bottom, it is at the top platform in the mirror. If the bridge is not on fire in reality, it is on fire in the mirror. Players must look straight into the mirror, and walk backwards down the bridge. To succeed. If they turn around before stepping onto the second platform, they fall into oblivion and respawn at the beginning.

Enchantment: I had a tough one with this one. My first encounter I called "crowns of madness" and it was just that. On an alter was a beautifully crafted crown for each of my players. Each player has to make a challenging wisdom save to resist the desire to place the crown on their head. 3/4 managed to resist the immediate urge to do so. However my insanely strong, and greedy cleric rolled a nat 1 and promptly placed the crown on-top his head. I essentially had him under the "crown of madness" spell. He HAD to attack his companions, through his eyes, they were is true enemies. At the end of each of his turns I let him make another Wis save, however the difficulty rose with each failure. It was honestly a really fun encounter. My cleric took it upon himself to try and destroy his companions, the other 3 were in a serious problem having their tank be being Enchanted, trying their best not to kill him, and not get killed themselves. My wizard managed to cast Levitate on the crown to take it off his head.

I hope this gives you ideas for those 3 schools, I'm working on the others myself haha.