In all honesty I can’t see why the Home Network Security would result in increased in CPU activity unless you have it scanning, otherwise as far as I’m aware it should be dormant (but I could be wrong). It is an on-demand function or as part of the Smart Scan.

You can try uninstalling that module/function - Control Panel > Programs & Features > Avast > Change - from the new windows uncheck the Home Network Security option. I would suggest you do a reboot after that and I don’t believe it will be revived.

That way you can confirm that any CPU activity is related/unrelated to the Home Network Security module.