Dear Matthias Hermsen,
Good day!!
Apologies for the inconvenience caused and please don’t worry, let’s work together on your concern and move towards a resolution path.
I understand your concern and to my knowledge, I am sorry to convey that there is no out of the box feature or setting in the PowerPoint for the web to create a new presentations from the custom PowerPoint template.
I agree with you having the ability to create a presentations from the custom PowerPoint template will benefit the users and suggest you to add your valuable idea as a feedback in the PowerPoint · Community (microsoft.com) which is the best place to share our ideas and improve the Microsoft PowerPoint product.
Moreover, in the SharePoint Online it’s possible to create a new file from the Content Types but adding the PowerPoint template or other Office template files to a Content Type will allow the new created files from the templates will be opened in the respective Office apps instead of opening the new files via Office for the web.
In this scenario, I would like to suggest you to using the Organization Assets Library, where you create a new presentations from the PowerPoint templates and here is the reference: Create an organization assets library - SharePoint in Microsoft 365 | Microsoft Learn
Appreciate your patience and understanding. Have a great day!!
Best Regards,
Sophia