What determines whether admin toolbar is shown to a logged-in user?

The admin toolbar is displayed for all users, including Subscribers.

If it’s not appearing on your site, then you are likely be using a plugin that changes this behaviour. For example, WooCommerce hides the admin bar from users who do not have the edit_posts or manage_woocommerce, capability. They have a support article on disabling this behaviour here.

Other plugins, such as membership plugins, might do something similar. You would need to check them individually.