I tested the Gutenberg PR build. https://make.wordpress.org/design/2021/03/03/testing-a-gutenberg-pull-request-pr/ for this PR: #36592

Templates screen
Clicking Add New I see this:

I am able to add a new template for "Front Page", "Archive" and "Search" but not a custom/general template.
Are there plans to extend?

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Template Parts screen
Clicking Add New I see this:

I am able to add a new template part: "General", "Header" and "Footer".
A template part can also be a sidebar. So I assume we can use the General for such use.

Or perhaps there should be a custom option in Templates and Template Parts.

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The above approaches should use the same method, but we see two different methods when clicking "Add New"
Templates open as a drop down. While Template Parts (parts?) open as a modal.

Should we go with one or the other approach (Modal or drop down) in the Templates and Templates Parts screen, so that we have a consistency when clicking the "Add New" button?

This can be looked at later on.