I'm not sure why it even makes sense to distinguish API/UI from other types of tests if you're developing a system / services full stack. This makes it even harder. You'll have to consider:
For both back and frontend, the more business benefit (unit < integration < system) them more effort it is to write tests for all use and edge cases.
We are developing test driven, so unit tests are of no question. Then we are moving to use spring boot integration tests for most of the heavy load stuff (DB, MQ, REST) because it's so stunningly easy to write those tests. Then we have the main use cases modeled as end-to-end system tests for both UI and Backend.
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