A word is a label for a definition. In language one label can be used on multiple definition, unrelated things even, or, many different labels can all point to the same definition.
In your example above, the word (or label) 'objective' is used in two different ways.
So in communicating, we simply have to make sure that the labels we both use are pointing to the same definition.
How am I doing so far?
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.