When you first launch the patched YouTube app, enable Flight Mode on your Switch. This prevents the app from immediately phoning home to Nintendo’s servers. The patched app should launch without the firmware update nag.
Alternative: Use Tinfoil (File Browser → SD card → select NSP → Install). youtube patched nsp install
Nintendo’s telemetry is aggressive. If you manage to install a patched YouTube app (even without going online), the Switch logs that the hash of the installed title does not match Nintendo’s server. The next time you connect to the internet for a game update, your console is flagged. Result: A permanent console ban from online play and eShop access. When you first launch the patched YouTube app,
This is the most common method shown in modern videos for patched Switches. Alternative: Use Tinfoil (File Browser → SD card