Sebastian.
I would be patient and wait to see if there are any taxes at all to pay.
Either way, I do think it's rather ungracious to have entered a competition, where the terms and conditions are stated ("6. Taxes. All federal, state and/or local income and other taxes and duties, if any, are the winner's sole responsibility"), and then when you win that ~EUR20,000 prize you blame the competition organisers because your government, the one you elected, tax the prize.
Here are your options:
1. Wait for the prize and if you don't want to pay the taxes, then just don't accept delivery;
2. Tell Keysight you can't accept the prize now, and they'll re-draw, just like they did yesterday;
3. Offer the prize to someone else in return for them paying any taxes directly on your behalf plus some consideration of your choosing for your trouble.
4. Pay any taxes and sell the scope at a significant profit.
None of these have any downsides for you.
There are an awful lot of people who would love to be in your position, to say you're sounding rather ungrateful would be an understatement. What a tough First World Problem to have to deal with!