> The removal of in-video ads.
You can pay YouTube for ad-free viewing... not doing so and stripping out the ads is dangerously close to "I just want this for free, so I'll steal it"
> Prevent YouTube from tracking your play/pause/seek activities.
A little bit of a tinfoil hat issue here, but it's fair if this sort of analytics bother you (it doesn't bother me).
> Restore picture-in-picture functionality.
Picture in picture works just fine on Windows and Android without a YouTube Premium account. Is this something specific to iPhone?
> The videos don’t stop playing if you switch to another browser tab.
On mobile, web videos are paused when you switch tabs or apps regardless of the website. Not something YouTube can control, and certainly not something YouTube is intentionally doing (unless you count Google and the decisions Chrome makes, and there is definitely something to that). What YouTube is doing, as I'll elaborate on in the next point, is stopping you from resuming the content after you have switched away from that tab. On all other websites, as long as they do nothing to prevent it, you can resume your video in the background by going to your media controls and hitting the Play button.
On desktop, this is not an issue, whether you have YouTube Premium or not. YouTube does not pause or stop videos when you switch tabs.
> You can choose the audio-only stream to keep the music playing when Safari is in the background.
As I hinted above, the crux of this one is that YouTube has deemed that background playback is a paid feature of YouTube Premium. I think this is silly, but it is their policy. Feel free to work around YouTube's technical restrictions on this topic if you want, but I return to exhibit A, that you can skip the ads and the restrictions if you sign up for YouTube Premium.
In the Flash days, making it use HTML 5 was (afaict) a quality of life change. This extension seems a bit sketchy at best. On the other hand the fact that the entire thing seems to be Apple ecosystem only probably says more about the Apple ecosystem than anything else (as I've said, this is mostly unnecessary on other platforms).
EDIT: PS: I would love if Chrome and the other browsers reversed their decision to auto-pause HTML5 video when you switch tabs or apps on mobile. It just feels like a way to push native mobile apps over web apps for no reason. I understand the risk potential of allowing this on the open web, but I think a permissioning model can work here to reduce the risks.