okay, this is what I just did in order:
Went to Logitech's site and downloaded the "Wireless Gamepad F710 Connect Utility."
Uninstalled the (malfunctioning)device in device manager.
Started the connection utility.
As per the utility, unplugged the receiver, took out one battery, plugged in the receiver, replaced the battery.
Utility says "Completed" and Device Manager shows an Xbox 360 Controller for Windows in device manager.
I haven't rebooted my pc yet because after seeing that "install" process I distinctly remember doing that at least a couple of times back when I first received the controller. Even though the utility said it was successful and device manager said there was a controller, it still showed it as an Xbox 360 controller like it does now. Driver date is 12/6/2019 but it says the driver provider is Microsoft, doesn't that mean that it just installed the built-in one from Windows 10?
What Windows version are you running? If Windows 10, which build version?
Windows 10 Home Version 21H2 Build 19044.1526