re: "If I am a US company contracting someone in the EU, does VAT apply?"
You don't need to worry about VAT.
VAT might apply to the fees European-based freelancers pay. But you don't need to do anything different.
Kimberly S. wrote:
If I am a US company contracting someone in the EU, does VAT apply?
Here are the VAT rules from the EU freelancer's view: https://europa.eu/youreurope/business/taxation/vat/cross-border-vat/index_en.htm
Selling services to customers outside the EU
If you provide services to customers outside the EU, you usually do not charge VAT. However, if the service is used in another EU country, that country can decide to charge the VAT.
So there will be no EU VAT.