Collector Crystals are the next level of Starlight gathering after Relays. You can place/break these crafted Collector Crystals at will (in contrast to the ones you find in large Shrines). These can be made from Attuned Crystals with high stats to become the most potent sources of Starlight available. The biggest motivation to use Celestial Crystals over Rock Crystals, or to refine the Size, Purity and Cutting of any Crystal, is to make powerful Collector Crystals that you can link to your Celestial Altar. This could allow you to craft at noon, craft in the middle of a rainstorm or for accelerated transmutation.
The best way to think about how a Crystal’s stats affect the performance of a Collector Crystal is to use a jeweler's analogy. In the end, all stats matter if you’re just concerned about producing the most Starlight possible.
Size - the larger the size of a Crystal, the more Starlight it can gather (the more surface area it can collect light from).
Purity - You can gather all of the Starlight in the world, but it won’t do you any good if the Crystal is occluded or cloudy. Purity is one of the most punishing stats if low, but also one of the least rewarding if absolutely perfect (a purity of 90% versus 100% leads to only about a 5% difference in Starlight). It is the most difficult stat to min-max, but conversely, also the least required.
Cut - Lastly, Cut determines the resulting focus of the Starlight coming out of the Crystal. You can gather all the Starlight in the world and redirect through the purest crystal, but if the Cut isn’t good, the light won’t be focused.
Attunement effects what rituals a Collector Crystal is capable of accelerating and what nights the Collector Crystal will be most efficient. In general, if a Collector Crystal is just for general Starlight production such as transmutation, linking to an altar or linking to a Lightwell, then you will ant to attune it to a “Bright” Constellation (because those are the ones that most commonly appear in the sky). On the other hand, making a Collector Crystal attuned to Pelotrio is suboptimal because Pelotrio shows up only once or twice a month (the Crystal is only at max strength those nights - unless you are specifically looking to accelerate a Pelotrio ritual). However, a Collector Crystal’s sensitivity to its attunement can be mitigated as detailed below.