How can I keep Safari and other apps from interfering with YouTube streaming?

Very simple...

What is very likely happening, in the scenario that you describe, is that a webpage that you open in Safari contains embedded video content - that autoplays as soon as the page loads. This embedded autoplay content will pause an existing playing video stream from another source - such as the YouTube App.

Unfortunately, whilst now having considerably enhanced capabilities over previous versions, iPadOS is still not a true multitasking OS. As such, it can only play a single video stream at one time.

The only available mitigation, which works in some cases, is to change the following setting in iPadOS:

Settings > Accessibility > Motion > Auto-Play Video Previews - toggle to OFF.

This refinement should help in many (but not all) circumstances. If you are using your iPad as a video source in a teaching environment, you might be better advised to use a second device whilst surfing - if nothing else, to avoid the possibility of inadvertently switching to “inappropriate” content. You might not have any warning as to the embedded content before appearing on-screen.

I hope this helps to effectively explain the unforeseen behaviour that you observe - the possible mitigation - and usage considerations.

My previous advice, to install a suitable Ad-blocker App, remains applicable. I recommend 1Blocker-X as it is very effective in suppressing salacious and/or other unwanted content within Safari.

Youtube often include “Ad-breaks” within their streamed content - and as frustrating as it is, there’s nothing that can be done to prevent it. Youtube, now a commercial platform, make a lot of revenue from Ad materials inserted into otherwise “interesting” content.

Ad content from various providers can be intrusive - whether served via you browser or internet-based App. Often the only way to suppress Ad content is to subscribe to the platform - where the streaming platform offers subscription-based service in lieu of paid third-party advertising.