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.

TIL Thank you pal, it perfectly works!