I'm running a modified version of Tyranny of Dragons where the Cult has splintered into three rival dragon armies—one entrenched around Old Owl Well, one fighting viciously near the Sword Mountains, and another holding the city of Luskan. While these factions are technically united in their goal to bring Tiamat into the world, their coordination is shaky and driven by internal rivalries. Recently, however, the factions opposing the Cult—like the Harpers and the Lords’ Alliance—have suffered a string of unusually precise defeats: ambushed retreats, intercepted supplies, and critical plans falling into enemy hands. It could be coincidence, but the timing is just too perfect. The players are tasked with uncovering who’s feeding the Cult this information. This side quest introduces a layer of espionage and mistrust: a spy or even a network of spies embedded within the resistance. The party must navigate secret meetings, decode intercepted messages, follow suspicious NPCs, and figure out who’s truly loyal. Some suspects may be innocent, others corrupted, and one might even be a double agent playing both sides. I want this side quest to explore themes like paranoia, trust, and ethical gray areas—how far are the players willing to go to protect the alliance? I’d love help fleshing out spy NPCs, red herrings, magical and mundane spycraft, and memorable investigative scenes to really bring this arc to life.

You have an interesting side quest going on here! 

Corrupted individuals gathering informations could be Innkeepers, tavernmaster and merchants that the Cult pay or blackmail.

Double agent could be one of them also feeding the Cult's enemies crucial informations.

Or a member of the Cult who is a Lord's Alliance or Harper spy.

Or Cult sympatisants being secret agent from Waterdeep Red Sashes or Force Grey.

Mundane spycraft could involve spyglass, scroll message using messenger creature, Cryptex requiring to unlock making a puzzle or ability checks skill challenge 

Magic specraft could involve Thought Bottle, Scroll with Invisible ink, Sending Stone, Scrying device and the like.

explore themes like paranoia, trust, and ethical gray areas

If you really want this paranoia et. al., the actual spy can be non existent.   The other group literally got very lucky.   If there is no actual spy, the Paranoia will go through the roof as no one can find anything.   

Ambushes are working, not due to luck, but the victims only have a few paths to use, so the enemy is basically having roving groups set up for ambushes 24/7 on the only paths available.   

 intercepted supplies are not via spies, but are large gatherings so dust/noise/destinations are clear to determine.

As for critical plans falling into enemy hands, make them so simple/obvious that even if they are not falling, they can easily be figured out.   But have a few plans per the ambush/supplies be included in the loot.  That is not spying, but just bad COMSEC. 

Drop clues that there is no spy, but the paranoia will discount and even ignore them.

Basically such egregious and bad choices are made.  not actual spies.  It just appears to be spies because after all, how can anyone be "smarter or more devious then us".

Throughout history lots of spies actually did not exist, it was stupidity and hubris that made it appear that their where spies.

A good way to play on paranoia is to spread rumor that a party member might be secretly working for the Cult.

Then plant false evidences pointing in that direction and watch suspicions grow : )

Or, you could have a couple of NPCs join them, from the different factions. They are all very friendly and helpful, maybe even saving the players lives once or twice, possibly making personal sacrifices. However, one of them is awfully suspicious, and looking into it only makes it seem more like they are a spy. However, they actually just have something else (romance, maybe) going on and they are not actually a spies. The real spy is another one of the NPCs, the favorite, friendliest, and while they are investigating, the spy plants info that frames the character for spying. The culprit might even try to get the framed character to join the cult.The trick to espionage type things is to make the culprit someone the characters like, and always having someone they like less to seem like the culprit. That type of thing always creates tough choices for the characters. 

The problem with that kind of twist is that it's been used so often in movies and TV that the players are highly likely to anticipate it.

Maybe take one of the players aside and see if they would be willing to actually be the spy. Maybe take all of them aside and, even if none of them are willing to play the part, let them wonder if any of the other players agreed.