They want you to use a solid state switch because of the fan load, and because none of the relay switching smart switches offer any kind of timedown operations.
If I understand what you want to do, you want to have a 3 speed adjusting switch that times out and shuts off 15 minutes after you give it the command to shut off?
Not gonna happen, brother. That's too much for a wall switch to do, and so precise it'd never make it to manufacture.
What you CAN do is wire a smart switch in circuit AFTER a sensing proximity switch.
This way you'd walk in the eroom and the lights would come on automatically.
The smart switch would be powered.
Then you can say "Alexa, turn on the fan".
When you leave, you've set the proximity switch to shut off after 15 minutes of inactivity, so it'll power down your lights and fan automatically.
I don't know how you already control the fan speed and didn't look at your links, but I will now to see if any of it changes that approach.
