This is expected behaviour as your navigation is pointing to homepage page sections. Its not working on CMS template as your template doesn’t know anything about the sections you are trying to go. You can try to create a copy of your navigation that you will use on your template page. You have already ID’s on your sections so you will point to these. You need to set your new navigation pointing to external page

and in URL you will place your URL from published site (homepage) followed by hastag and idName
eg. https://webflow.my-sitename.io#projects
I thing that that should work but I can’t prove it. Maybe someone will come with better solution.