Another user created this thread previously explaining this use case:
https://forum.builder.io/t/how-to-add-inline-text-editing-for-a-custom-component/4936
Effectively, there is no way to use the Inline Text editing feature that's present in the OOTB Text component, and you cannot similarly replicate it from the source of that component, since it would seem that BuilderState is not able to be modified by custom components.
If there is a means to handle this, let me know but I think this is a common enough requirement (and expectation) by developers that this would be possible.