Ultimately trying to be eligible to work in the EU

I’ve been reading through the forums and articles on Golden Visas, and I’m trying to get an understanding of what eligibility I have to work within the EU with certain GV options. Does the Portuguese Golden Visa allow me to live/work anywhere in the EU? Or is it only after citizenship is granted?

What about the Caribbean visas like St. Lucia?

I’m sorry if this has already been answered! Thank you!