Pretty sure the project wizard just pulls the home folder and adds "New Unity Project".
To set up the assets folder, perhaps create a new project and manually create the folders. Then export that as a package. The new project wizard gives you a list of packages to import, so I guess if you can work out where that list comes from (probably a mix of some editor defaults and the location where asset store packages are found) you can have that project folder package imported into all new projects.
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