Word Templates not showing up in SharePoint/Teams after being added via PowerAutomate

Question

I've been trying to setup a flow that automatically mirrors (read: copies and creates new) Word templates from one Teams Channel to another. The goal is to have them appear in the "+ new"-dropdown in sharepoint and teams (see screenshot). "+new"-dropdown in Teams

I believe I managed to find the path to the folder in which to put the template-file, which is: https://yourcompany.sharepoint.com/sites/YourSiteName/Freigegebene Dokumente/Forms The "Freigegebene Dokumente" should be "shared documents" in english afaik. Here comes the caveat: When I upload a template-file via powerautomate, they do not show up in the "+ new"-dropdown. When I then try to manually add the same file via the "+ new"-dropdown, it tells me that a file with that name already exists.

Am I missing something? I fully expected this to just work.

What I am trying to get running so that the bigger solution can work is this:

1. Manually trigger a Microsoft PowerAutomate Cloudflow
2. Get information about a specific file in SharePoint (a .dotx MS-Word template)
3. Get the content of that specific file
4. Create a new File in the */Forms folder with the same name and content as seen in the screenshot.
5. Be able to create a new File in SharePoint (and Teams) from that template via the "+new"-dropdown

The two parameters used are:

@outputs('Dateieigenschaften_abrufen')?['body/{FilenameWithExtension}']

and

@body('Dateiinhalt_abrufen')

Screenshot of the flow

After running this flow, I expect to have a new template to choose from in the "+new"-dropdown in SharePoint. That is not the case.

I know that there is something uploaded, because if I try to manually add the template via the "+new"-dropdown
manual upload in "+new"-dropdown

I get this error message:
Error Message on manual upload