Sharepoint Site button to create new file in document library

MorePowerBI I will be interested in hearing if a developer has a solution for this. I'm not aware of a way to add/remove options in the +New menu on the homepage. I would offer up an additional solution to you though that would not require your users to navigate to the document library to add this new document from your custom template. You could add a Document Library web part on your homepage. You can customize how much displays of what is in the library if you don't want a long list of documents taking up space. When you edit the web part properties in the panel that displays on the right, be sure that the toggle switch for "Show Command Bar" is turned on and your viewers will see the +New button in that document library web part and be able to select the template from there.

The + New option you are referencing is intended to add parts to the architecture of your site while the template is related to the architecture of your document library. You could have users who don't have edit options for the webpages on your site who would never see that +New button. However, if they have edit permissions on the document library, they would see the +New in the document library web part allowing them to add a new file from the homepage.