I'm not an expert, but I was curious so I did 15 minutes of digging and this is what I found. Take it in context.

Wikipedia's Usage share of web browsers page references two sources for stats: StatCounter and NetMarketShare.

StatCounter is an analytics tool for web site operators. They cover their methodology here: https://gs.statcounter.com/faq#methodology . To quote:

Our tracking code is installed on more than 1.5 million sites globally.

Their installation guide explains that they use a small JavaScript snippet embedded into the site's HTML.

Firefox blocks this if enhanced tracking protection is set to strict. Discussion on Hacker News: https://news.ycombinator.com/item?id=34502986 . Some commenters there also said that uBlock origin blocks it. I have not confirmed.

NetMarketShare also refers to collecting data from user browsers and requiring JavaScript. https://netmarketshare.com/methodology

I would be interested to see server-side statistics based on HTTP user-agent from major global sites like Wikipedia, but I was not able to find that. I imagine spoofing user-agents is less common than ad blocking and tracker blocking

Edit: Found Wikimedia's browser stats:

https://analytics.wikimedia.org/dashboards/browsers/#all-sites-by-browser/browser-family-and-major-hierarchical-view

Linked from https://en.wikipedia.org/wiki/Wikipedia:Statistics#Analytics