Based on the doc,
To insert merge fields into your Experience Cloud site email templates,
From Setup, enter Email Templates in the Quick Find box, and select
Classic Email Templates. Next to an email template, click Edit.
Under Available Merge Fields, from the dropdown menu, select the field
type, and then select the field. For merge fields specific to sites,
select Network Member Fields.
Copy the merge field value into the body of the email template.
There is no mention of Lightning email templates and so it looks like community merge fields are not supported yet.
Also see known issue according to which the workaround listed is
The option to use these template types is not fully supported for Site (Community) emails. Please use Classic templates if using merge fields is required for the emails intended purposes.