If you have a raspberry pi or some device laying around that you're happy to act as an always-on-server you could set it up as a Layer 7 firewall using something like Nginx to act as a reverse proxy for SSL/TLS interception.

Throw this into some LLM on research mode and I'm sure you could get some step-by-step instructions for setting it up.

I suppose it's not much different to a PiHole but instead of filtering out ads you're filtering out shorts.

Don't their shorts go under https://www.youtube.com/shorts/

Maybe you can just block all URLs that falls under /shorts/

Not router level, but "Enhancer for YouTube" has "Hide shorts" in its appearance preferences. Available on Chrome, Firefox, and Edge.

If I was a concerned parent, I'd just install and hide the extension from the bookmarks bar.

The downside being that it doesn't affect native YouTube apps for mobile devices...