Site editor: Align template part creation with regular template creation

[jameskoster]

Currently template and template part creation UIs do not match:

Add template

This flow uses a dropdown menu:

Add template part

This flow goes directly into a modal:

We should update the template part creation flow to match the template creation one like so:

Asking the user to immediately name the template part is an unnecessary friction. Depending how they choose to proceed when presented with patterns we can either:

1. Use the name of the selected pattern as the template part name.
2. Use "Untitled Header" when they elect to start blank.

[jameskoster]

Just noting that this may not be necessary if we implement #36613.

[jordesign]

As of WP6.3 both Template Part/Pattern and Template Add flows use a modal - so I'll close this as resolved.