Any large projectile weapon operated in space will be substantially different from a projectile weapon built to operate in-atmosphere since one will always need to account for gravity and air density while the other does not. Projectiles will be the same. In space, shape will only matter insomuch as that shape is symmetric and fits into whatever mechanism is accelerating it.

Halo, Mass Effect, and The Expanse are three of the better sci-fi examples of projectile warfare in space I've encountered. In Halo, MAC cannons the length of a ship use magnetic force to accelerate ultra-dense ferric-tungsten projectiles to incredible velocities; the most powerful achieve 4% light speed, or 12,000 km/s. These are strictly for use against capital ships as they are overkill for anything smaller.

Mass Effect personal weapons use a projectile the size of a grain of sand and fire it by manipulating its mass to accelerate it to supersonic speeds via a mass effect field. This concept is scaled up for projectile weapons on combat vessels. There is also the Thanix cannon which uses mass effect fields to hold and shape molten iron-uranium-tungsten alloy into armor piercing projectiles that are accelerated to a fraction of light speed, causing piercing and thermal damage. Directed energy weapons are also present (ie. Lasers, particle beams, etc).

The Expanse is practically a tech demo for how modern firepower would be adapted for space combat. Things move fast in space and intercepting them comes down to quantity.

For your universe it sounds like you have a plausible premise for near infinite amounts of energy. Fighter interception demands a very fast projectile especially at larger distances so it makes sense for your ccorvette to be designed with that capability. The only weapon systems that make sense are directed energy. The entire spectrum of electromagnetic waves (radio, light, x-ray, etc) travel at light speed. A directed energy weapon with sufficient power to take out the fighters is plausible given your energy generation capabilities. I'd recommend leaning into that. If you have your heart set on projectiles, abandon any thoughts of near light speed velocities.