This is straight up misinformation. First off, it's perfectly legal.
LinkedIn does browser fingerprinting. It's the same thing Google and Meta do. It's how Google Ads is shifting to a post-adblocker revenue stream.
Browser fingerprints show fonts used, audio codecs, WebGL render data, processor, operating system - enough that if you add up several factors together, it makes a statistically unique fingerprint. it does NOT scan applications on your computer. It can't. It DOES scan which browser extensions you have running (if they affect page loading).
If you check your email and then close that and go to Google in an incognito window and search for porn - Google will fucking know what you're looking at. Gmail and all Google apps all fingerprint, and then you'll notice how Google ads trackers are on most sites online? Yep. That's how they track you.
Use a VPN? Use an ad blocker? Great - Google doesn't care. Google can track your fingerprint.
See your own fingerprint - check how it know it's you visit after visit.
https://fingerprint.com/
https://coveryourtracks.eff.org/
https://amiunique.org/