It monitors the Network as such, I don't believe it specifically runs scans, it is active all of the time monitoring the network.
So it will be constantly checking new network connections.
Unfortunately there isn't much for anyone to work with here as we know nothing about your Avast Program or the Network Inspector and Firewall settings.
I rarely get any notifications or interference from the Network Inspector, my settings screenshots are attached below.
Avast UI > Protection > Network Inspector
Avast UI > Menu > Settings > Protection > Network Inspector
Your Firewall settings will also have an impact depending on what you have set as a Trusted Network.
I doubt it's the firewall as nothing has changed. It keeps saying "connected to new network", even now after a single boot.
Scan for devices and monitor this network is off like what you've shown me in the first picture as well.
This started happening since the last avast program update. Like even as soon as that update was installed it did "connected to a new network", and did a scan at startup.
I'm using the latest avast free antivirus, 24.3.6108.
I could disable it as you showed in the image, but it's strange that it's a new behaviour since that update.