Increase light brightness with time

Home automation question here.

I have some generic HomeKit lights that can be dimmed and change color. I have a HomeKit hub.

I’d like to have one of the bulbs turn on to a set color and then gradually increase brightness over about half an hour.

I have a shortcut that can do this (with a caveat — see below): It sets the bulb’s color; takes minutes of the current time, subtracts 30 if it’s over 30 (to get a number from 0-30), multiplies by three (to get 0-90), adds 10 (to get 10-100); and sets the bulb’s brightness to that number.

If I could run this shortcut at set intervals — say 6:05 am, 6:10 am, 6:15 am etc. — the bulb would go from off to 25% to 100% over the course of half an hour.

But I can’t figure out how to run the shortcut as a home automation. What am I doing wrong? Or is there a better approach? (There must be!)

I have HomeBot (works nicely for setting the color and brightness, even without documentation for what hue numbers mean), Home Assistant (haven’t used), and a bunch of the other Shortcuts apps (ToolboxPro, Pushcut) in case those are helpful. I don’t have a Pushcut server and would rather not fiddle with that if I can avoid it.

Thanks!