Looks like newspaper4k uses headless Chrome. You could try loading the Bypass Paywalls Clean extension and browsing the pages directly.
I regularly use it (in Firefox) without even thinking about it. Only notice when I send someone an article they can't access.
No, just this example code from their site:
My mistake was not knowing where newspaper4k fits in the stack. They're wrapping it with Playwright, which it seems you could do here.