Switched routers and suddenly main machine wired to the router could no longer be seen by other devices on the network

To help troubleshoot some intermittent Internet issues, I switched routers from an Asus model to the Cox Panoramic Gateway, which I had previously been using in bridge (modem-only) mode with the Asus, the idea being to test with just the Cox equipment. Everything went as expected, except that my PC wired to the router could no longer be found by other devices on the network. I looked at "Settings->Network & internet" and clicked Properties, and the "Network profile type" section that normally appears at the top of the ensuing page was totally missing, so I couldn't switch it from the "Public" type. I looked at adapter properties for this Realtek PCIe 2.5GbE Family Controller, and it appeared as below:



I don't know how it was configured before I switched routers, but checking the likely suspects including "File and Printer Sharing for Microsoft Networks" restored the missing "Network profile type" section, allowing me to choose "Private network" and thus restore connectivity to other devices on my network. As you can see, I do use Hyper-V and VMware, and my VMs were working fine before I switched routers and continued to work fine afterwards, including before I made these changes. I never touched any of these settings before now.

Can anyone explain what happened behind the scenes to screw up my networking after I switched routers?

Did I correct this in the right way?

1. reset network adapters Reset Network Adapters in Windows 11 Tutorial

2. Reset network components with @FreeBooter bat file. Unzip and run as administrator.

First, I don't know why it happened. Before I give the final resolution, I want to note the solution I described wasn't really proper though it seemed to work perfectly fine. It resulted in the following configuration with two "Connections" bound to the "Network":



I surmised from this page that the only "Connection" (adapter) that should be bound to the network is the Hyper-V Switch:


This emboldened me to delete the Hyper-V switch and recreate it. Deleting it restored the "Network profile type" section to the Win+I "Network & internet" settings, and I was able to switch back to private network there. For the settings in the screenshot above, only "Ethernet" was bound to "Network". Recreating the Hyper-V switch flipped the situation and left only the Hyper-V switch connected. It removed all the items like "File & Printer Sharing" from the Ethernet adapter and enabled them in the Hyper-V switch. The Ethernet adapter settings looked just like the screenshot in my OP, but this time, everything worked, and my main PC was visible to other devices on the network. Checking Win+I "Network & internet" settings again, "Private Network" appears under "Properties":



However, clicking Properties reveals that the "Network profile type" section, the one that lets you switch between Public and Private modes, has again gone missing (it's normally at the top, above "Authentication settings"):




While the section is missing, at least the "Private network" status survived the Hyper-V Switch creation. I have no idea why connecting temporarily to a different router reverted it to public. I also don't understand why Ethernet appears here instead of the Hyper-V Switch, which presumably would have the "Network profile type" section, but that's just the way it works, apparently.

Anyway, problem solved.