I created my own site package and thus the complete configuration into my own EXT. outsourced.
Now I have included in the database a template on the root page around the StaticTemplate of the EXT installed by me. and manage it.
Can this be outsourced to the site package?
Yes, there are two ways to achieve that:
Export the template and place it in the folder Initialisation/data.xml of your sitepackage see https://docs.typo3.org/m/typo3/reference-coreapi/master/en-us/ExtensionArchitecture/CreateNewDistribution/Index.html#database-data
Instead of placing your template into the database you can include your TypoScript without a sys_template record explained here https://usetypo3.com/did-you-know.html#c554