Ok, some addition.
Earlier I used CCC to clone system from internal only because I couldn't install Monterey on external SSD by standard means (via installer). The installer seemed to copy system files just fine, then asked to reboot, and then after some progression on apple progression bar screen it somehow kept to abandon the task and rebooted back to my internal drive without finishing the installation and without any error.
Well, as it turns out, the culprit was the SSD's type of connection during installation. It was connected to USB-C previously, now I've connected it to USB-A and installation suddenly went just fine. After installation I reconnected the SSD back to USB-C port and it works fine. Don't know why it happens (I think it's a problem of the current macOS installer), but maybe the trick will help someone else.