My iPhone running Safari and uBlock Origin lite is able to do this. I don't have the youtube app installed. I don't even think the ad blocker is necessary for background audio, but I don't want to see ads.

1. Go to youtube.com in the browser, play the video, switch back to the home screen. Video playback will stop, which is a good default behavior.

2. Swipe down from the top of the screen which brings up "Notification Center" which somewhat strangely contains a playback control for the browser.

3. Press play. Audio resumes. If it's part of a playlist, you don't have to manually advance, it will play automatically.

No ads, no youtube premium subscription, no "desktop mode", no sideloading, no additional apps other than the beloved ad blocker.