You said you were using an "Eye Adaption" Plug-in. Disable that first to make sure the issue is not caused by that.
At last you have several knobs to tweak the outcome. I recommend you use a balance of each depending on the settings.
Reducing Shadow strength to 80% simply reduces light intensity by 80% where the shadows are supposed to be. Simple, however when you have indoor levels it might give poor results inside the buildings.
These are the key. More information on environment lightning: https://docs.unity3d.com/Manual/GlobalIllumination.html#Environment
I personally use different light settings for indoor and outdoor levels. I don't change anything when the Player is entering a small building, but when the Level changes from an outdoor environment to a large bunker or a cave I have a set of triggers in the map that set different Environment Lightning values when you pass through them. Lerp between two triggers to make a slow transition.
Here is what it should look like.
All mentioned settings turned off:
Only Environment reflections:
Environment reflections and Environment lightning (Skybox):
Sun shadow strength 80% indoors (Nonsense):
A nice balance of all settings (Outdoors):
You also have the possibility to use additional lights with shadows disabled and bake them to tweak the lightning to your needs but going over that would be too much for this answer.