That's a totally valid question; I myself wouldn't like to start using a service just so it would be shut down later.
Answer: if company made API publicly available and you're following their terms of usage, then it's completely legal for Osprey to use. But if the API isn't exactly publicly available and company didn't publish documentation for it, then it's illegal. Where does Osprey come in here? From what I see, it's a mixed bag.
When you open
BrowserProtection.js file, there are all API URLs listed along with parameters. There's SmartScreen URL and by searching the web I couldn't find any information about Microsoft giving devs access to their SmartScreen APIs. The developer most likely captured requests made by Microsoft Edge along with parameters and added it to the extension. That isn't legal per se, because he never got Microsoft's approval to use it. Same goes for GDATA, Emsisoft and Bitdefender.
But not everything in this extension is illegal. Security DNS servers he uses as a source are completely legal and have their API URLs publicly available. They need to have them publicly available because DNS-over-HTTPS simply works this way.
Now... what are the consequences for Osprey? Of course security companies can always send him DMCA notice on Github, cease & desist letter or even start a lawsuit against him. But in reality, I don't see that happening. Though they could change the API URL in the future, stopping Osprey from checking URLs with them, or they could start using some kind of authorization. This obviously won't happen for now, but if the extension becomes really popular, that could become problem.