The queen can now additionally move like a knight. What do you think the new point value is?

too many.

This is known as an amazon
Its estimated worth is 12 pawns.
en.wikipedia.org/wiki/Amazon_(chess)

I'll just jump over your Queen as well. @GCH82

15. It covers a 5*5 area already.

checkmates would be easier

it's over 9000!!!

15-20 because of the mates

200 if the piece is called Xena.

My guess would be something like 12 points initially, increasing significantly as the game progresses.

it would 9 plus 3 plus 3 which is 16.