Cross-posting my answer from Godot forums for posterity:
Godot 3.x only supports one DirectionalLight with shadows at a time.
In Godot 4.0, using more than 1 DirectionalLight will always have a significant performance impact, especially if shadows are enabled on more than 1 DirectionalLight. Doing so will also worsen shadow quality, as the shadow map texture will have to be shared for multiple DirectionalLights.
As a conclusion, in Godot 4.0, even if it doesn't look physically accurate for your game, I strongly recommend sticking to 1 DirectionalLight for best performance and quality.
PS: OmniLights with shadows are not intended to be used as a replacement for DirectionalLights. You could increase the shadow atlas size (or use a distant SpotLight instead), but it will never look ideal since there is only one shadow "split" to speak of.