Yes, this is a real pain. My workaround, which irritates me but works, it to first paste into Word, the select all copy and paste into Evernote.
Its awful but it works. Pasting from the same text copied from Word yields the correct spacing in Evernote. Seems like Evernote is not translating line breaks in HTML to maintain correct formatting.
BTW, Apple Notes has the same problem.
Easy to reproduce: On MacOS, Copy from any Google Doc, Paste into the Mac Evernote App. Every line has an extra spacing. Cross Platform has nothing to do with it.