If you feel it with your nail it's too deep to polish yourself.
You need a scratch remover. It's expensive and need alot of experience to not harm the glass.
It's a special polish machine for glas. It heats up the glass so much that it melts the sharp edges of the scratch and moves the molecules in the glass to make it smooth.
Everyone that delivers glass to windscreen shops have this or should have it. There is scratches in glas all the time in transport and handling. This machine removes them before they are sent out to windscreen shop.
I work with this so I know.
For the interested ones, this is the machine:
https://www.glaswelduk.com/scratch-repair