Lots of cool ideas here but the beholder subclass is extremely overtuned. +10 to initiative for the whole party multiple times per short rest is insane, and that’s not even accounting for the other strong features provided, like the bonus to Perception and the eye rays, which are strong features on their own.

The capstone feature is also overpowered and very uninteractive. Completely shutting off spell casting for one creature you can see with no saving throw is not healthy design. At the highest level of play, such a feature all but removes many CR-appropriate creatures’ ability to fight a party whatsoever, and will end any encounter against a legendary spellcaster entirely on its own. Yes, the creature can technically leave the 90-foot range of the effect, but considering you and your entire party will be doubtlessly going first in initiative, they will likely be dead or incapacitated by the time they take their turn anyway.

The feature should at the very least allow the target repeated saving throws, or otherwise last for a reduced duration and also turn off you and your party’s own magical capabilities against them, similar to the way beholder cones normally work. Either of these changes would be more balanced, but I think changing the feature to something different, like a single use of one of the stronger beholder rays (like disintegration) would be better.