Mac TV app on Sonoma unable to see Home Sharing on my network

Summary: The TV app on two Macs are unable to see Home Sharing that's hosted by a third Mac, while other Apple devices on the same network can.

Here's what's shown in the TV app on both client Macs (an Intel iMac and Apple Silicon MacBook Pro) when I click on Home Sharing.

I've confirmed that:

• All devices are on the same network.
• The client Macs can see and access the server Mac on the network for both file and screen sharing.
• All devices are signed into iCloud using the same Apple ID.
• The server (Intel-based Mac Mini) has Media Sharing turned on, and the Home Sharing box is checked and shows the proper Apple ID.
• Other Apple devices (iPhones, iPads, and Apple TV streaming boxes) on the same network, and logged into iCould using the same Apple ID, are able to see and play videos from the Mac Mini using Home Sharing.
• All Macs (clients and server) are on the latest build of macOS (Sonoma, 14.3).
• All Macs (clients and server) are fully up to date on their Apple Apps, including the TV app.

Troubleshooting steps I've performed, without success:

• Quitting and restarting the TV app.
• Logging out and then back into iCloud on each Mac.
• Rebooting both the server (Mac Mini) and the client Macs (iMac, MacBook Pro).
• Turning Media Sharing and Home Sharing on the server (Mac Mini) off and on again.
• Switching between wired (gigabit Ethernet) and wifi connections to my home network.
• Clicking on my Apple user ID at the bottom of the left pane in the TV app to confirm the app has the proper account info.

I'm out of ideas. Anyone have troubleshooting steps I haven't already covered above?