Google should be returning the highest quality results. If thats a paywalled newspaper, it should not be excluded.
However, I do think some kind of tag, similar to [AD] could appear next to the result, warning you not to click it, [PW] or [LW] for paywall and loginwall.
If I continue to run into the same paywall, I would consider buying into it. If I bought content, I would want it to show up in search. I wouldnt know I want to buy it, if I dont run into it first.
Then Google should work on a way to connect your purchase with their system or give you ability to inform them you’ve purchased a subscription so that only you get to see search results from that paywalled website, and not others.
However, I do think some kind of tag, similar to [AD] could appear next to the result, warning you not to click it, [PW] or [LW] for paywall and loginwall.