I have the same settings as yourself.

"Check for updates, but let me choose whether to install them" 

I also unchecked the option "Use a background service to install updates" as this then forces the UAC to ask if I really want to update. It basically means I do get a second chance to back out of update if selected by accident.

I'm currently using two versions 128.14.0esr (I had to get that version from https://ftp.mozilla.org/pub/thunderbird/releases/ because it was not offering it - I was offered upgrade to the current release). I'm also running beta 144.0b1

I've not had any pop ups or any other sign that mention/prompt an update is available for a long time, but I've always had the options via 'Help' > 'About Thunderbird' and also via 'Settings' > 'General' > Updates section.

Which means it is checking for updates, but it seems it's up to me to check either of those locations to know if an update is available.

There did used to be a green dot which appeared on the 3 line menu app icon when an update was available but I've not seen that in a while. I'll try to find out if that was stopped at some point.

I used to get a popup window notifying me of an update, but, like you, I haven't seen this in a while. Waiting on what you find on this. Thanks for your response, Steve H.