by default it doesn’t proxy the video stream you are getting from YouTube. it just extract the link to that stream and sent it to your browser and then you browser plays that stream URL which points to google’s server so google is able to see your IP address.
however there is an option called “DASH” if you enable this option the stream would be proxied by your invidious instances. this options is disabled on most of the public instances because of high bandwidth usage.
You could use instance on my VPS it’s not blocked yet. However it’s http only :/
It’s always heart breaking to see IA in trouble :(