Well they should have been automatically installed on the new device. I'd suggest starting over with a factory reset (you mentioned reset, but I don't know if that means factory reset) - Settings->System->Advanced system settings->Factory reset (follow the prompts). Once it reboots and starts the setup process, make sure you're linking to the same email address that's displayed on the other device under Settings->System->About.
One other note: Don't use any kind of VPN while you're setting up the device. It seems strange to me that at times you're seeing different things on the website. The apps are linked to your Roku account (not any particular device) and that information is stored on Roku's servers, so if you're logged into your Roku account and search the channelstore website for an app that's already installed, it should show that it's already installed. When I'm not logged in and search for an app that I've already installed, it gives me the option to add it and then wants me to log in when I click the "Add app" button. Your seeing a disabled button makes me wonder if the website thinks you're in a region where the app isn't available, which can happen if you're using a VPN or anything that masks your location.