Calling TOS camp shows a misunderstanding of the term, and is a kind of tone deafness to style.
It was melodramatic in the way that TV westerns and cop shows often were.
What set Trek apart from most TV fantasy was that it was so earnestly similar in tone and overall style to contemporary-set network hour dramas at the time. Whereas series like Batman and Lost in Space played with a broad wink to whatever adults happened to watch them.
^^this
Multiple facets to "camp" exist, but I don't think too many would place TOS, or most Trek, in the same, eh, camp, as Batman in terms of campy runarounds and exaggerated aspects of real people and aimed squarely for outrageously comedic intent. Trek plays with these on a different level, but Trek has generally eschewed our universe and for the sake of believing their universe's drama, whereas Batman operates alongside it or plays into it - generally for self-conscious laughs, save for the odd cliffhanger for which some could be genuinely chilling... until these were replaced by increasing levels of dumb that drove viewers away.
Batman66 definitely shows intentional camp for risible comedic intent. TOS was asking you to believe the improbable as serious, because we really don't know what's out there - even more so in 1966. There are definite facets to both shows and definitions.
Add in the passage of time and materials cost, etc, and it's easy to see ideas retroactively applied that might not be the case as it's easy to discover how expensive TOS was to make at the time. Lots of people say nowadays it looks cheap, without fully understanding of the details of the time (which is inevitable after a certain point), we've all been on both sides of this phenomenon, etc.
TOS definitely can be called
melodramatic. That's what all sci-fi needs as character drama can too easily be overdone and without the plot inducing some dramatic effect (the underlying melodrama), you've got nothing for the characters to react to. Balance seems to need a bit of both character and plot-based grounding, even in the unknowns and technical absurdities (not comedic) of what may be out there in outer space. Getting drama to feel authentic out of the situation is a more difficult request as it's too easy to overact or render any dramatic buildup moot and coming across hokey (melodrama).
Most importantly: TOS was even sold in advertisements that it was adult sci-fi, as means to directly differentiate it from kid and truly campy shows like "Lost in Space" (which is fun, but the differences speak for themselves.) It rarely was a comic book or live action cartoon, which LiS was - as well as Batman66.
The A-word is mentioned outright: "Adult".
TOS is also more akin to "televised theater" as in "televised stageplay", which was simply the norm of the time - you guessed it - describes "camp" as well.
The other elephant in the room regarding word definition, as "camp" has multiple definitions: It can be described as intentionally silly for comedic effect. It can be described as "low budget". Add in a few more and it's easy to see where conflation begins. But in tonal quality? Many of the TOS (and TNG) episodes that have that more often than not tried being no less serious but failed, inducing accidental mirth from the audience. Big difference. Trek, even season 3, was not intentionally trying to get Batman's ratings.
Another show comes to mind, "The Man from UNCLE". From day one it was exploring technically outrageous things, as the spy genre was wont to do. But it's pretty much season 3 that tries to blend in "the Batman effect" and viewship vanishes. Unlike other shows, TMfU tried to course-correct, and season 4 is wholly underrated, but the viewers did not return. (And as the Batman comic was generally seen as serious by fans, you can bet credits to navy beans* that fans who tuned into the silliness balked. And to think season 1 had moments of stern seriousness before season 2
flanderized it all by making everything silly for the sake of it, which is when ratings started to drop, hence the retooling for season 3 (but forgetting to reverse course and not be so hokey, so ratings continued to drop.)
* That I'll accept as intentional camp, in an episode that was trying hard not to go Batman on everyone's heiney.
Then add in intentionally-comedic episodes like the Tribbles episode or 1920s gangster world (which took an improbable and cost-saving idea once played seriously and now used it deliberately for laughs and that episode I would absolutely call "campy", but it's more of an exception to TOS and not the general standard, which helps because if every episode felt like Batman-lite, would TOS really be held to any regard nowadays? Conversely, look at how serious Batman became since the 1990s and how many throw out the 1966 version as being stupid. Fun fickle things, audiences are... )
Long story short, everyone's not wrong.
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