Hi Alan,
A Realtek Bluetooth Code 31 on Windows 11 almost always means the Bluetooth half of a Realtek combo card cannot load because it is mismatched with the Wi-Fi half. On these Realtek M.2 cards the Bluetooth radio rides on the same module as the Wi-Fi adapter. The firmware and driver set are shipped together by the PC or motherboard maker. That is why Device Manager says the July 11, 2024 Bluetooth INF is the latest, yet the device still fails. Updating only the standalone Bluetooth INF from Realtek rarely fixes Code 31. You actually need the exact Wireless LAN + Bluetooth package for your model. I know you prefer not to touch the Network Adapter, but in this case the Bluetooth driver depends on it. You are not changing any network settings, just reinstalling the paired package so Windows can load the Bluetooth stack.
Temporarily disconnect the PC from the internet. This prevents Windows from injecting a generic driver while you clean things up.
Open Device Manager. Expand Bluetooth. Right click your Realtek Bluetooth device and choose Uninstall device. Tick Attempt to remove the driver for this device, then OK. Now expand Network adapters. Right click the Realtek Wi-Fi adapter on the same card and do the same. Restart the PC.
Install the official Wireless LAN or WLAN + Bluetooth driver package from your PC or motherboard support page for Windows 11. Vendors usually label it Realtek Wireless LAN Driver or similar, and inside it are both Wi-Fi and Bluetooth drivers that are version matched and HVCI compliant. If your machine is a custom build, use the motherboard vendors support page for your exact board model. Avoid the generic Realtek site for this one.
Reconnect the internet. Open Device Manager and confirm the Realtek Bluetooth device loads with no yellow icon. Bluetooth should now be working and Code 31 should be gone.
A quick note about the Logitech K360: That keyboard uses a 2.4 GHz Unifying USB receiver, not the Realtek Bluetooth radio, so its crash after the October update is a separate issue. Once Bluetooth is healthy, if the keyboard still will not show up in Logi Options+, we can tackle that next.
If you want, tell me the exact PC or motherboard model and I will point you to the right OEM package to install so you do not have to guess.