10.15.6 update broke Thunderbolt USB 2.0 hub

I have a 2020 13" MBP running Catalina 10.15.6. I have a Thunderbolt Display that I've used for years with my old MBP in clamshell mode, with an optical USB mouse and a receiver for a Logitech wireless keyboard plugged into the USB hub in the Thunderbolt display. I have also used it with Catalina 10.15.5 without this issue.

After I updated to 10.15.6, the laptop no longer recognizes the TB Display's USB 2.0 hub if I plug in the display (via Apple TB-to-USB-C adapter) after the laptop has been booted. It only recognizes the hub if the display is plugged in when the system starts up. If I connect to the display post-boot, the system recognizes the display and that works, but not the HIDs plugged into it. I have to use the laptop keyboard and touchpad.

Bottom line, I have to restart every time I "dock" with the display in order to use the mouse and keyboard plugged into the display. This is annoying, to say the least, especially when it (mostly, see below) worked fine before the update.

The TB Display firmware version is 26.2, Port Micro Firmware version is 2.0.7.

PS. I was also (before the update) experiencing audio issues somewhat similar to those described here, which is why I need to unplug from the display to record audio.