Re: "Sharing Wi-Fi from Macbook M4 Air to iPad or vice versa"
Am no expert in this area, yet your post has gone unanswered so far, and deserves some response:
You can see: How to share your Wi-Fi password from your iPhone or iPad
I don't know whether or not you can
Use an iPhone or iPad to connect your Mac to the internet - Apple Support in those circumstances.
Eg: says:
Note: "This feature may not be available with all carriers.
Additional fees may apply. Contact your provider for more information".
More info,. if needed: How to set up a Personal Hotspot on your iPhone or iPad - Apple Support
NB: also says:
"Certain apps and features that require a Wi-Fi connection might not work while using a Personal Hotspot. For example, you might not be able to make an iCloud backup or upload photos to iCloud Photo Library or Photo Stream".
Other available info: Trouble-shooting: Connect to the internet with your Mac - Apple Support
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Re: "if I get my Macbook registered and my iPad unregistered, can I share my Macbook Wi-fi to my iPad?"
Seems you would need an Ethernet (cable to modem) connection, and Mac would not be able to "sleep".
See details: Share the internet connection on Mac with other network users - Apple Support