How do I set/get third party settings on a content block?
ThirdPartySettingsInterface is used by config entitiy types:

Interface for configuration entities to store third party information.
A third party is a module that needs to store tightly coupled information to the configuration entity. For example, a module alters the node type form can use this to store its configuration so that it will be deployed with the node type.

BlockContent is a content entity type, and doesn't implement the interface, hence the error.