Thank you so much!
The anaglyph/abberation effect was made using a simple shader that adds an offset to the red/blue channel of the sprite (and rendering the sprite to a seperate viewport so the shader won't affect things near the sprite).
This is basically the whole fragment shader:
COLOR.ga = texture(SCREEN_TEXTURE, SCREEN_UV).ga;
COLOR.r = texture(SCREEN_TEXTURE, SCREEN_UV + offset_r).r;
COLOR.b = texture(SCREEN_TEXTURE, SCREEN_UV - offset_b).b;
The background and spawn/start screen effect was made using Godot's CPU particles.