Running the Chrome extension on your own device? Yep that's OK. But republishing full articles on the web accessible to all - no chance. They have a DMCA link at the bottom to "excuse" themselves.
What if you use a Chrome extension to train a ML model to format the article, then publish that model back to the web? At least it would allow users to remove ads and other cruft from articles.
In what country?
as legal as Google Cache, probably.
Google Cache respects paywalls and robots.txt, it seems Outline does not.