Hmm. I think I've got somewhere.
I did a 'Reset Settings' in the settings. Made no difference. The HID service still showed (no access) and the Web IDE etc failed.
But then I did a 'reboot without loading any software', and, now, the Bluetooth LE Explorer doesn't show the HID service at all.
AND, now, the Web IDE and app loader work fine... Including showing the correct debug output in the JS console.
I did try doing the 'Rebooting without loading any software' previously, and that made no difference. Apparently resetting the settings first made a difference.
Now, I can reboot it normally (loading all the default apps) and it still works fine.
So, that's a result, but very odd. The settings were all what I thought they should be, and look to be the same now. Maybe there are some hidden settings which were wrong, which were fixed by the 'reset settings' and then a reboot.
Not knowing the details of how things work, my guess is it may be that the unavailable HID service was upsetting the Windows Chrome Web BT, but the Android Chrome didn't care (your Android phone doesn't support a mouse, for instance), so didn't get upset by it. So, that's why Android worked, but Windows didn't.