Currently, according to the following Atlassian documentation, only Space Administrators are entitled to edit Space Templates:

Only space administrators can create or edit templates in Confluence Cloud.

If you don’t have Admin permission for a space, you won’t see the Look and feel card when you go to Space settings and you won’t be able to create templates.

• https://support.atlassian.com/confluence-cloud/docs/create-a-template/

It would be a good addition to allow non-admin users to edit templates by creating a new Space Permission which would allow users/groups to edit/create Space Templates.