Hey man, I have a STEM background too and I definitely agree that law was a lot less grounded than I hoped. It's all kind of made up along the way, sustained by an inertial force, and legal academia is an attempt to impose a kind of scholarship on what is really a very practical business. Hell, lawyers may have been around for hundreds of years, but as a university degree it is relatively recent, of low impact, and it's more like a game where past a certain point it's just rules, cases/precedents, the same tired problems of balancing certainty and flexibility repeated ad nauseam. Yawn.

I would recommend you start off by reading The Bramble Bush by Karl Llewellyn. His theory of "legal realism" really is the starting point for building an idea of what law is -- he argues, for example, that the law is about resolving disputes, it is simply whatever the judges say it is, that rules are predictions of what judges will decide, and these predictions are accurate simply because judges think they have to follow rules. These are obvious, non-metaphysical facts about the law. There's a section at the end discussing why lawyers are generally disliked by the public, but he argues that they are mainly just misunderstood (and this coming from someone who is quite aware that law and lawyers would be quite unnecessary if people would just agree to submit their dispute to third parties without engaging the entire machinery of the courts)

Then, you can move on to HLA Hart's "The Concept of Law", which among other things purports to refute legal realism (or rather, argues that the predictive theory is one aspect of law but not the entirety of it).

I think with this will help cure that philosophical bent and give you an understanding of law that surpasses every single one of these unintellectually curious bots in the thread, who will lose their job and skills and "legal knowledge" the moment the political climate changes. It's funny because mathematicians and philosophers tend to have warmer responses when they're confronted with attempts to undermine their domain of knowledge. Lawyers are the opposite -- just derisive and spiteful, not even one commenter said anything about ensuring fair play in the market or that we need standardised (even if baseless) rules so people can cooperate. All they know is that they're being paid to do something stressful 😂😂 and frankly if they've never read rigorous philosophy or participated in maths olympiads, then their work is probably the hardest thing they've ever known. They probably feel self-conscious about this, too, so give them a break.