There's an issue to support adding third party settings to sections: #2942661: Sections should have third-party settings, but it would be great to also support third party settings for individual components (blocks) within a section.
For example, modules like Block Class and Field Formatter Class use third party settings on block config entities to allow the user to add arbitrary CSS classes to a block. It seems that the only way to do this with a Layout Builder block is to modify the settings form for the individual block plugin you want to modify and store the configuration along with the other configuration for that block.