It's not surprising to find clustered sentiment from a slice of statistically correlated language. I wouldn't call this a "personality" any more than I would say the front grill of a car has a "face".
Deterministically isolating these clusters however, could prove to be an incredibly useful technique for both using and evaluating language models.
Those that do find correlations between self-reported personality and actual behaviours tend to find those to be in a range of something like 0.0 to 0.3 or so, maybe 0.4 if you are really lucky. Which means "personality" measured this way is explaining something like 16% of the variance in behaviour, at max.
On top of that, a confounding issue is that human nature is to anthropomorphize things. What is more likely to be anthropomorphized than a construct of written language - the now primary method of knowledge transfer between humans? I can’t help but feel that this wishful bias contributes to missing the due diligence of choosing an appropriate metric with which to measure.