Could someone please tell me if I can somehow license production of SkyWater 130 in my country?

its open source. Not able to understand your requirement

Well, there are several sorts of open source licensing schema out there, and current SkyWater Docs / Specs are being updated, so I just wanted to know if there's any type of formal request necessary for this to be all legal

https://www.skywatertechnology.com/contact-us/ this way you can query more information