It’s a strange one!
As I understand it, the process is that the client (PC, TV) fires off a DHCP request and any available DHCP server will respond. There’s then a bit of quick to-ing and fro-ing while they check the proffered IP address isn’t in use elsewhere on the network. In the event that the Windows PC can’t find a DHCP server, it becomes a DHCP server and gives out 169.254.x.x IP addresses to any other device that will listen. You say that you can see the Netgear allocating IP addresses but clearly the Windows PC isn’t getting an IP address, so it’s not.
As I understand it, the process is that the client (PC, TV) fires off a DHCP request and any available DHCP server will respond. There’s then a bit of quick to-ing and fro-ing while they check the proffered IP address isn’t in use elsewhere on the network. In the event that the Windows PC can’t find a DHCP server, it becomes a DHCP server and gives out 169.254.x.x IP addresses to any other device that will listen. You say that you can see the Netgear allocating IP addresses but clearly the Windows PC isn’t getting an IP address, so it’s not.