The problem they're addressing is that some sites they were scraping from have begun instituting measures to stop them. The site went from working beautifully to working barely at all, with most sources either loading incredibly slowly or failing to load at all. I followed the discussions a bit on their discord, and it seems like the first recommendation was for users to host their own proxies. From what I see on the site's initial splash, that still is one of the recommendations. I'm guessing they also rolled out the browser extension as an alternate method for users who don't want to set up a proxy, since they were getting tons of people on thsir discord complaining about it being too hard or whatever.

But yeah, who knows if the extension is safe. The project is open source, so you can always examine it for yourself. But at that point you may as well just host your own proxy.

Edit: looked into it a bit more; the extension's originally proposed purpose seems to be to get around CORS restrictions on certain sources. Seems the original proposal was here: https://github.com/movie-web/movie-web/issues/581