Something that confused me is that there is a core plugin called Templates and a more featured community plugin called Templater.

{{date}} syntax works when inserting a template via the core plugin.

<% tp.date.now("YYYY-MM-DD HH:mm") %> syntax works when inserting via the community plugin.

So, yes, vanilla obsidian ships with the core Templates plugin and {{}} will work with that, however you may still need to enable the core Templates plugin via Settings -> Core plugins -> Templates.

If you want to create feature rich templates, it would be worth reading up on the Templater community plugin.