Looking at Ask Ubuntu, the "Sponsored by AWS" is... large on mobile. For reference, this is how it would look on an iPhone 12 (I'm using device emulation for the screenshots hence why I'm signed out, but the "Sponsored by AWS" is still just as in my face on a real mobile device).
I'll quote the AWS sponsor announcement for Ask Ubuntu, as that is how I noticed this (by pure chance, I haven't checked other sponsored sites on mobile recently apparently)
What else changes? Not a thing! Borrowing from the original MSE announcement on sponsorships:
First — sponsors do not own these Q&A sites. Sponsors work alongside our communities who ultimately build these sites. Communities ask the questions; communities create the tags; communities conduct elections as they do now, and we are not renaming our current sites like a garish sport stadium to the highest bidder. Any ads a sponsor submits still have go through our crazy-strict ad editorial process… as it has always been. Companies do not have access to personal data, and all Q&A content remains irrevocably licensed under Creative Commons for sharing and attribution.
Sponsorships are a tool that our clients can use to let folks who could be interested in their products know about them in a non-intrusive way.
So... um... having "SPONSORED BY AWS" as the first thing on the page below the page name (and the menu bar) doesn't exactly seem "non-intrusive" to me. It seems more like a banner ad.
Of course, I have a proposed solution: make the sponsor on the same line as the site name. This is what is done on "desktop". The sponsor is still displayed, but it doesn't look like an in-my-face banner ad. Considering the sponsor adds no useful information to me (when viewing the page, specifically), it doesn't need a dedicated line on the page prominently displaying it.
Something like this, but with the big orange box shorter (I made this quickly in paint.net)
Some of y'all might notice I originally posted this on Ask Ubuntu Meta. Turns out this affects several sites (three I've seen, maybe more?), so that is why it goes here.