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No, physics is never vague. Some problems are currently computationally intractable beyond a specific level of accuracy (like predicting the weather more than 2 weeks out), and some questions we do not know answers yet but expect to find answers to in the future (like why did the big bang happen). But there is never an element of the mysterious or spiritual or "man can never know".
Popular science physics often gets mysterious, but that is a failure of popularization. Like the observer effect in quantum physics, which is often depicted as a literal eyeball watching the photons go through a double slit (?!). This may cause a naive viewer to mistakenly start thinking there is something special or unique about the human eyeball and the human consciousness that physics cannot explain. It gets even worse - one of the most popular double slit videos on youtube for example is "Dr. Quantum explains the double slit experiment" (not even gonna link it) which is not only laughably misleading, but upon closer examination was produced by a literal UFO cult, and they surreptitiously used the video to funnel more members.
Or the "delayed choice quantum eraser experiment" which confounded me for years ("What's that? I personally can make a choice now that retroactively changes events that have already happened in the past? I have magical time powers?"), until I grew tired of being bamboozled by all its popular science depictions and dug up the actual original research paper on which it is based. Surprise! Having read the paper I have now understood exactly how the experiment works and why the result is sensible and not mysterious at all and that I don't have magical powers. Sabine Hossenfelder video on youtube debunking the delayed-choice quantum eraser was the first and so far one of only two videos I have seen in the years since that have also used the actual paper. This has immediately made me respect her, regardless of all the controversy she has accumulated before or since.
Isn't the idea that the world is never vague, kind of an assumption? What if some are, and some aren't?