Thanks for support.
Uninstalled it completely as described in the ComfyUI desktop user guide, and made a new fresh install. This time it’s working fine when restarting from Manager, or closing the window. Perfect 
Root cause maybe: I figured out that using a custom installation of comfyui Pinokio to get user settings and models made this new installation bugging. So I’ll try fix it manually by copying manually some settings, and changing Comfy config file to point to Pinokio’s models directories.
Still have another issue, with Manager saying “Your ComfyUI is too OUTDATED!!!”. When checked Manager version, it says “Manager: V2.51.9”.
Same problem described here, but on Windows 11 for me https://forum.comfy.org/t/the-installed-comfyui-does-not-have-a-git-repository/465