For what it's worth - and I'm not saying that LinkedIn is doing this for the right reasons - I can imagine a frontend QA team wanting to do this to understand how prominent certain extensions are for users of various parts of their product, correlating those extensions against frontend bug reports, and using that to guide QA procedures with real-world extension sets.

When you're literally the company that invented Kafka for your clickstreams, "everything looks like a nail."

(More likely, though, this is an anti-scraping initiative, since headless browsers are unlikely to randomize their use of extensions, and they can use this to identify potential scrapers.)