One of my gripes with youtube at the moment is that they break my adblock filters to remove shorts more often than they break the filters stopping the actual ads.

I use an addon for firefox called "Hide shorts for Youtube™". Works just fine.

I naively searched in the mobile app settings for a way to turn off shorts, before realising there will not be one.

You can't turn it off entirely, but if you keep using "show less shorts" from the 3 dot menu it eventually goes away, mostly...

If you're on android it's better to just use revanced or something