This is really cool, I like the concept a lot. There is one thing I could use clarification on, maybe if I wasn't so new to 5e I would know already. This incantation system that you use.... "To cast one of these incantations, you must expend an incantation slot. You regain all expended incantation slots when you finish a long or short rest." .... Is that to say that even at level 20, you can only use 3 incantations between rests? That seems like incredibly limited power, especially since the bulk of the rest of the class features also relate to these celestial energy points. Additionally, at a glance the number of celestial energy points seems very limited. At level 20 you start the day with 6 points, and if evenly distributed you have 3 of each type to play with. I can use all of my starting sun points to get:

Target a non-magical weapon you are touching. For 1 hour the weapon sheds bright light in a 20 foot radius and dim light for an additional 20 feet. In addition, the weapon becomes a magic weapon with a +1 bonus to attack and damage rolls. In addition, the weapon deals an extra 1d4 radiant damage.

Which for sure is a cool effect. But at level 20, even if all 6 of my points are sun at the time, I'm using HALF of them for that. and expending one of my 3 incantation slots. I dunno. I could be misreading the intent of your words, and be digging a hole for myself. I'm very interested in hearing the clarification though, as I like the concept a lot and would play it if it ends up seeming viable. Thanks!