What happens when Internet Connection Sharing is enabled?

Question

Windows

There is a PPPoE Internet connection. This connection is shared to a small home network using ICS, checking the "Allow other network users to use this computer's Internet connection" checkbox. What is happening at this moment and is it possible to repeat this operation in another way?
For example, there is also wifi hostednetwork, through which you want to distribute the Internet also to wireless network participants. But it seems that only one checkbox can be put on the connection.
Combining Lan and WiFi into a bridge does not help (or I'm doing something wrong).
When sharing, the LAN interface is assigned the address 192.168.137.1 and it becomes a gateway for other members of the local network. But, even if hostednetwork assigns an address from this range and does the same statically on the phone (since IP is not dynamically distributed in this situation), packets from wifi to the lan segment do not go. Perhaps you need to register routes, which I did not succeed.
What can be done in such a situation? So far, we have managed to solve the issue by installing WinProxy and setting the proxy and port in the phone. Works, but feel like a crutch.
About bridge. In my opinion, merging Lan and Wifi does not work, since hostednetwork is a virtual WiFi adapter with which the merger does not go, and regular WiFi "does not know" about it.
I'm completely confused, please help me sort it all out.