Thanks for the PR @albarin! The issue here is how to extend this menu with more templates provided by third party devs.

Currently the template creation does quite a few tasks from enhancing menu items dynamically, fallback content and more, and uses the info provided by DEFAULT_TEMPLATE_SLUGS, so we need to be careful with the changes we'll make. I think what we need is to extend without changing the DEFAULT_TEMPLATE_SLUGS. Maybe instead use a new variable/setting(probably server side) and maybe change useMissingTemplates to add them in the end of the core suggestions? That would be my first thoughts. --cc @jorgefilipecosta

Currently the template creation does quite a few tasks from enhancing menu items dynamically, fallback content and more, and uses the info provided by DEFAULT_TEMPLATE_SLUGS, so we need to be careful with the changes we'll make. I think what we need is to extend without changing the DEFAULT_TEMPLATE_SLUGS. Maybe instead use a new variable/setting(probably server side) and maybe change useMissingTemplates to add them in the end of the core suggestions? That would be my first thoughts. --cc @jorgefilipecosta

Thanks for your feedback 🙏 Makes sense that it shouldn't be possible to remove anything from DEFAULT_TEMPLATE_SLUGS.
I've been exploring your suggestion, not sure if it's the right way to do it, but what about using the block_editor_settings_all to introduce a new setting allowed_template_slugs that would be filterable (not sure about the naming though ), something like:

function gutenberg_default_template_slugs_settings( $settings ) {
	$settings['allowedTemplateSlugs'] = apply_filters('allowed_template_slugs', []);

	return $settings;
}

add_filter( 'block_editor_settings_all', 'gutenberg_default_template_slugs_settings');

and then on the useMissingTemplate doing something like this:

export const useAllowedTemplatesSlugs = ( editSiteStore ) => {
	return useSelect(
		( select ) =>
			select( editSiteStore ).getSettings().allowedTemplateSlugs,
		[]
	);
};

const allowedTemplateSlugs = useAllowedTemplatesSlugs( editSiteStore );
...
const missingDefaultTemplates = ( defaultTemplateTypes || [] ).filter(
	( template ) =>
		[ ...DEFAULT_TEMPLATE_SLUGS, ...allowedTemplateSlugs ].includes(
			template.slug
		) && ! existingTemplateSlugs.includes( template.slug )
);

Thanks again! 🙌

Yes, something like your above comment would be one approach. We'd need to explore a bit here though with some PR(s). Maybe another approach would to have a value that also lives in store that keeps the extra template types, and introduce an API like addTemplateTypeOption or something like that to be more declarative. It will need more thought, but I'd go with the declarative approach for the first try.

The issue here is how to extend this menu with more templates provided by third party devs.

I'm not sure if there is an issue about this, but if not could you create one? Thanks!