get_the_terms inside save_post gives old terms

This issue shouldn’t happen if you’re using the classic editor, however, if you’re using the block/Gutenberg editor which uses the REST API, then that issue can be fixed by using the wp_after_insert_post hook instead.

Excerpt from

The new action wp_after_insert_post has been added to WordPress 5.6
to allow theme and plugin developers to run custom code after a post
and its terms and meta data have been updated.

The save_post and related actions have commonly been used for this
purpose but these hooks can fire before terms and meta data are
updated outside of the classic editor. (For example in the REST API,
via the block editor, within the Customizer and when an auto-draft is

So try using wp_after_insert_post:

add_action( 'wp_after_insert_post', 'get_the_terms', 10, 3 );