How do plugins store their configuration/field data?
Sounds like the answer is "the data is probably the config table... but it could also be anywhere else depending on the implementation." In the commerce_license example I noted, instances of LicenseTypes on Product variants get their own entry in commerce_product_variation__license_type, where the data for that instance is stored in the license_type_target_plugin_configration column. Just like data stored in the config table, this is a hex blob which, when decoded, is the config field data as a serialized array.