Scratched Front Screen topic

Hey everyone, i need your input on something.
Long story short my phone fell from my hands this morning from pocket height and slided on the wooden floor for around a meter or so. Due to dust on the floor i inherited a few scratches.

I was wondering if anyone tried any toothpaste/polish/windex etc on the front screen to smoothen a bit the scratches.

I haven't seen this anywhere so i'm not sure, but does the screen have any kind of coating similar with what the lens cover has?

Thanks for the input and have a great year everyone.