Saving custom post types post_meta over REST-API fails

The register_meta() function is defined like so:

function register_meta( $object_type, $meta_key, $args, $deprecated = null )

And the $object_type (as of now) has to be post for all post types. So use this:

register_meta( 'post', 'survey_data', ... )

See the // {comments} in the code below, which I copied from here:

<?php
// The object type. For custom post types, this is 'post';
// for custom comment types, this is 'comment'. For user meta,
// this is 'user'.
$object_type="post";
$args1 = array( ... );
register_meta( $object_type, 'my_meta_key', $args1 );

UPDATE

If you’d like to limit the meta to a certain post type, use the object_subtype parameter like so: (that parameter was added in WordPress version 4.9.8)

// Add survey_data meta support to `survey` post type in REST API.
register_meta( 'post', 'survey_data', array(
  'show_in_rest'   => true,
  'object_subtype' => 'survey',
  ...
) );

// Add survey_data meta support to `my_cpt` post type in REST API.
register_meta( 'post', 'survey_data', array(
  'show_in_rest'   => true,
  'object_subtype' => 'my_cpt',
  ...
) );

And as you can see, just duplicate the same register_meta() call for other post types. But the $object_type needs to be post, even for Pages (page post type).

UPDATE

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