I’ve done that before, but then I run up my cellular data use because it stays connected to my iPhone.As long as your carrier plan supports ‘Personal Hotspot’ you just have to turn it on in Settings.
Settings>Personal Hotspot… then, Settings>WiFi>Auto-Join Hotspot.
How to set up a Personal Hotspot on your iPhone or iPad - Apple Support
A Personal Hotspot lets you share the cellular data connection of your iPhone or iPad (Wi-Fi + Cellular) when you don't have access to a Wi-Fi network.support.apple.com
It seemed like the way you described it would automatically connect to your hotspot only when you left the house. Maybe I misunderstood.