The nature of swarms is defined in the Monster Manual:
The swarms presented here aren't ordinary or benign assemblies of little creatures. They form as a result of some sinister or unwholesome influence. A vampire can summon swarms of bats and rats from the darkest corners of the night, while the very presence of a mummy lord can cause scarab beetles to boil up from the sand-filled depths of its tomb. (MM, p. 337, bold added)
The commonality to all the examples given is that a swarm is a group of animals that is influenced by a single malign intelligence. Cranium rats fit this mold quite well also, although in their case the single malign intelligence is formed from their collective minds merging into one:
Cranium rats are no smarter than ordinary rats and behave as such. However, if enough cranium rats come together to form a swarm, they merge their minds into a single intelligence with the accumulated memories of all the swarm's constituents. The rats become smarter as a result, and they retain their heightened intelligence for as long as the swarm persists.(Volo's Guide to Monsters, p. 133)
So the very thing that allows cranium rats to act as a swarm (unlike mundane rats who aren't under the influence of some other creature) is that their minds all alter to become part of a single collective mind, and become more intelligent as a result of their shared consciousness. But a central feature of wild shape is that using it does not alter the intelligence or consciousness of the Druid. This is reflected in the description of wild shape:
Your game statistics are replaced by the statistics of the beast, but you retain your alignment, personality, and Intelligence, Wisdom, and Charisma scores. (PHB, p. 67)
The wild shaped druids could definitely gain mental abilities that they usually don't have (e.g. the cranium rat's telepathy), but any feature of the cranium rat that alter's the creature's intelligence will not work on the druid, since "you retain your... Intelligence." And it sounds like this altered intelligence is precisely what allows cranium rats to act as a swarm.
The group of druids definitely couldn't cast psionic spells
You claimed that the cranium rat swarm's psionic spells are not spells. They are.
the swarm can innately cast the following spells, requiring no components:
Other text describing them as "similar to spells" does not override the fact that to use this feature, the group of druids would have to "cast" a "spell." And unless the druids are 18th level or higher, when you are in wild shape:
You can’t cast spells (PHB, p. 67)
Jeremy Crawford also specified this in no uncertain terms.
Wild Shape says you can't cast spells. The feature doesn't care where those spells come from. You can't cast them.
The Rules Don't Support a swarm of Druids very well
Most of what I said above (other than the spellcasting part) is a logical argument that makes sense, but isn't definitive. You could argue that the cranium rat's communal mind feature is a case of "specific overrides general," and although druids don't usually change their intelligence when they are wild shaped, they would in this case (I believe this would be mistaken, but it is supportable). However, making this argument would mean you'd have to fundamentally rewrite several rules regarding swarms.
As a simple example, consider the fact that swarms have no rules for individual members of their swarm running out of hit points. You do damage to a swarm as a collective, and although damage does kill members of the swarm this is abstracted rather than precisely calculated (mainly abstracted by the fact that a swarm with half hit points does less damage when attacking). However, wild shaped druids change back into their natural form when they lose their wild shaped form's hit points. So when does this happen to the druids in the hypothetical swarm? Does it happen gradually, every time the swarm takes 2 hit points? Or does it only happen when the entire swarm's hit points are exhausted?
Similarly, if you rule that the wild shaped druids in cranium rat forms meld their intelligence when they are together, you should also similarly rule that a single druid wild shaped into a cranium rat who is around other cranium rats loses his or her individual consciousness, and instead becomes part of the cranium rat swarm's collective mind. Also, you should also cause them to be entirely controlled by any nearby mind flayer colony's elder brain, since this is also a feature of the cranium rat's unusual method of thinking. If this was your ruling as a DM, it might result in a PC becoming an NPC (possibly permanently) by virtue of them simply being in the vicinity of other creatures, which seems a dangerous ruling to make.
To sum up...
At the end of the day, the rules leave some wiggle room for you to pursue this idea, and the "rule of cool" definitely gives it some fascinating story possibilities (druids who form a bizarre elder brain like collective consciousness, and begin a fully new form of life in their collective community): but it contradicts many available rules, and directly goes against the intended nature of wild shape. There are many beasts whose minds are fundamentally different from those of humanoids: from the instinct driven lives of insects to the practically memoryless life of certain fish. But druids wild shaped into the form of these animals do not lose their memory or consciousness when they look like these beasts: and for the same reasons, they should not change their way of thinking to fit that of the alien and other mind of the cranium rat.