That's exactly what the Features module is for. Syncing partial config across multi-site instances.
The features module enables the capture and management of features in
Drupal. A feature is a collection of Drupal entities which taken
together satisfy a certain use-case.
Features provides a UI and API for taking different site building
components from modules with exportables and bundling them together in
a single feature module. A feature module is like any other Drupal
module except that it contains additional information in its info file
so that configuration can be checked, updated, or reverted
That means you would create a feature on your main multi-site instance which contains the paragraph type. Have it placed inside the modules/features/ folder. Related config will be added automatically. You then enable the feature (which basically is just another module) in another multi-site instance. The config will be imported into the database. On both multi-site instances you then export config as usual. Because every multi-site instance still is managed from its own config. Which then also contains the synced paragraphs config.
As soon as you add another field to the paragraph type on either multi-site instance Features will recognise the changes. You then can recreate your paragraph feature and import the changes on another multi-site instance (into the database). Finally, on both sites again export config as usual (which then also contains the paragraph types you've synced via Features). Features enables you to keep track of changes to a feature via built-in diffing, which after you recreated the feature (partial config gets exported) can be synced into the database on other multi-site instances again.
Of course Features also comes with a set of Drush commands to make your live easier.