I pay for YouTube premium.
So it really sucks when I google the name of a movie, click to play the trailer, and then it plays a pre-roll ad. This only happens with the movie trailers that you one click play from the search results. If I click on something that goes to the youtube domain or youtube app, it's fine.
I'd like no videos when I'm playing videos from google. My google account and youtube premium account are the same, so I'm not sure why it doesn't link.
Also, with chromecast, it's really annoying that they allow multiple users to put videos in the queue, but only have my videos be ad free. It effectively removes the multiphone feature because I have to look up and play (and ruin my recommendations) on my phone anyways. One premium users being connected should be enough to kill all of the ads.
I've also had ads rarely and randomly show up. If I had to guess, some "is this user premium" server was down, and it decided to default to "no", despite that being the explicitly frustrating experience for paying users.
I pay for YouTube Premium, do the steps you describe, and do not see that behavior.
You must be in another browser session that's not signed in to your Premium account. You're in incognito or on second browser. Just sign in to YouTube to fix it.
For anyone else reading: the issue happened on iOS Safari. I was signed in on the YouTube iOS app, and I was signed in on Google.com on Safari, so I assumed there wasn't anywhere else I needed to be signed in. But sure enough, I went to youtube.com in Safari and wasn't signed in. Tried it once after doing that and it worked. Will see if it solves it, seems likely.