So, I fixed the issue by following the "WinUI 101" guide (https://learn.microsoft.com/en-us/training/modules/winui-101/) that led me to adding the package that references everything I was missing. However, based on the content of the main guide page (https://learn.microsoft.com/en-us/windows/apps/get-started/start-here?tabs=vs-2022-17-10), something like that shouldn't really have to be done manually before the first run of the app.

For everyone having the same issue, what you've got to do besides the mentioned setup steps is:
In Visual Studio, with your project loaded, select "Tools" > "NuGet Package Manager" > "Manage NuGet Packages for Solution...". In the opened window, in the "Browse" tab, search for Microsoft.WindowsAppSDK , and install the latest version.