I would consider both definitions of 'objective' as being applicable to scientific inquiry. The first definition applies to the investigator who strives to be objective in gathering, analyzing, and drawing conclusions about data. The second definition is a property of things themselves, that they exist independently of thought, which science is also concerned with.Good!
The same with knowledge. If you strip away the requirement of observability as the only one and look closer at observability is it about objective. If you then look at the different versions of objective the most general one is this one - "expressing or dealing with facts or conditions as perceived without distortion by personal feelings, prejudices, or interpretations."
How? All perception or experience as in this one - "involving or deriving from sense perception or experience with actual objects, conditions, or phenomena" - doesn't mean observation as in science. That is these 2 to a varying degree - "of, relating to, or being an object, phenomenon, or condition in the realm of sensible experience independent of individual thought and perceptible by all observers : having reality independent of the mind."
So let me give you an example of something which is not knowledge in science, but it is knowledge in the soft end of social science as connected to psychology and human science.
How you do act, when as a professional in human general caretaking deal with another human, depends on how you deal with the private, the personal and the professional. But you can't observe this as per natural science. You can only to do it if you learn to be objective in the other variants, because it is not science as it is not of, relating to, or being an object, phenomenon, or condition in the realm of sensible experience independent of individual thought and perceptible by all observers : having reality independent of the mind.
It is knowledge in the mind about how different mindset works.
And as a professional in this line of work you have to be a human, personal, but you can't be private, and you have to hold that the other person might not be objective, but you have to.
There is more, but generally the joke is that you can be objective about the subjective in a limited sense, if you learn that.
You seem to make a distinction between what you call science, and what you call soft, social, or human science. For me, they are all part of the same science and must adhere to the same principles and standards.