Problem #1
Shadows are visible in Unity Editor, but not in the WebGL build.
This is usually caused by the distance shadows are visible from not being high enough if the quality settings for your WebGL build. So, simply go to your Project Settings -> Quality, then select High in the top right (used for WebGL), then increase the Shadow Distance till they’re visible for your camera/scene setup.
Problem #2
Lighting is drastically different in the WebGL build compared to the Unity Editor.
This is a bit of a weird one, Unity itself says Realtime GI is not supported in WebGL builds, but for some reason doesn’t automatically disable it, so, you have to do it yourself. Window -> Lighting -> Settings, then disable Realtime GI. It’ll take a minute to recalculate everything, Build & Run, and you should be good to go.
Cheers.