Macbook Air (13-inch, Early 2014) macOS Catalina 10.15.7
External monitor connected HDMI to Thunderbolt
Logitech K750 keyboard, M325 mouse
Running with lid closed (closed display mode), on power adapter, we logout then select sleep, the monitor goes dark, the monitor power button LED changes from blue (video signal) to yellow (no video signal). After 15-seconds, the monitor power button LED turns blue and the login screen is displayed. This happens without touching the keyboard or mouse. PRAM and SMC have been reset.
I’ve had this happen a few times on my 2019 Macbook pro running big sur. I use the same monitor with my windows computer as a second display and it doesn’t wake it up. I’ve found if I unplug the adapter (annoying) that it will usually stay asleep.
In lockdown for 5 days, so decided to try testing my MBA 2011 in configuration you’re using (as close as possible). I connected a monitor via thunderbolt port using a VGA-Thunderbolt adaptor. No wireless mouse, so tried with USB mouse, then with Apple Wireless Touchpad.
Initially had same reaction you had with wired mouse and touchpad. I have a “hot corner” defined to put display to sleep. Each time I used it, display went to sleep, power light went to yellow, then it woke up. Tried same using “sleep” under Apple power options (clicked on small Apple in upper left corner, then “sleep”). Same result. No idea what I did then, but after many times putting it to sleep using both main and secondary displays, it started working correctly. Now, after many restarts, I can’t get it not to work correctly. I’m totally confused.
I suggest you try putting it to sleep from both displays, with cover opened and closed, several times. See if that “shakes it out” as it has on mine.
Just a note on using this mode. Monitor is not supposed to stay on when lid is closed if MB is running on battery.
So far my solution has been to log out, click sleep, and turn the mouse off. The Logitech mouse and keyboard are connected using the Logitech USB Unifying Receiver.
I also use a Logitech mouse from the MX series. However the unifying receiver is in the Windows Computer and I connect it to my Mac via bluetooth. I do turn the mouse off before putting the mac to sleep and use the trackpad to enable sleep mode.