Loading a template from a CMS page

I’m working on a Magento 2.4 PWA system. The idea is to load a template from a CMS page.

I’m using {{block class="CompanyModuleBlockIndexIndex" template="Company_Module::index/index.phtml"}} in the CMS page, but it doesn’t load or render anything in the page. I know it does something because if the reference to the template is wrong, the system returns an error.

That’s all I’m doing. What am I missing?

Thanks.