I would like to ask for your advice on updating the module. I tried to update the module via Extensions → Updates → Download these updates and I got to this website, from which I am unable to proceed because my login is not working. Do I need to use a specific username and password?
I see, no worries. In this instance, you need not do anything. Moving forward, in the new infrastructure, we will be able to trim the list of modules you would otherwise see in the REMOVE section. Ultimately, the only modules you need to concern yourself with are the ones shown in the second screenshot. If you utilise all three, no need to do anything. If you do not use one or more of the three, consider removing them accordingly.
In this case, please note that the error is from the themes folder and not the modules folder your second screenshot shows. You would need to add the core_version_requirement: ^8 || ^9 to the .info.yml file in the theme. I however note that you are using the CERN OVERRIDE theme version 1.4. This is a very old version and might contain deprecated code (unfortunately we cannot see this because of PHPStan failing to run). If you know what exactly you have of customised logic, if anything, in your theme, please consider moving this to the newest version of the OVERRIDE theme to avoid any issues. If you are not actually using the OVERRIDE theme, consider simply removing it.