The problem with your pattern suggestion is that you should probably turn off all LEDs to avoid any having been left on from previous patterns. (LEDs continue to do their last command, so you want to explicitly turn them all down/off)
That might be harder with the Pico, less pins exposed and you’ve wrapped it in shrink-wrap (covering pads you’d have to solder to if one would work) and that also assumed you’d have a way to digitally power off the power and then somehow to turn it back on, separately.
So I’d add a real relay that Homenet can control. No pattern needed, cause no power.