Previously we could use a Composer to remove the getting started dashboard, which was fully supported by the core, what's the official process in V15?

I think you can deregister using an entry point https://docs.umbraco.com/umbraco-cms/customizing/extending-overview/extension-types/backoffice-entry-point

Maybe something like this

import { UmbEntryPointOnInit } from '@umbraco-cms/backoffice/extension-api';
import { umbExtensionsRegistry } from '@umbraco-cms/backoffice/extension-registry';

export const onInit: UmbEntryPointOnInit = (_host) => {
    // remove default dashboards
    umbExtensionsRegistry.exclude('Umb.Dashboard.UmbracoNews');
    umbExtensionsRegistry.exclude('Umb.Dashboard.RedirectManagement');
};