(not OP) I've thought about P vs NP a fair bit. Something interesting about 3-SAT is that, suppose you have N variables. Then there are 2^N combinations for the bits, so obviously a brute-force search is exponential-time. But what's interesting is that each clause of 3-SAT gives you a combination of 3 variables which doesn't work, effectively pruning 1/8 of the entire tree. So each clause implicitly prunes an exponential-sized chunk of the search space. There's just no way to take advantage of this.
With 2-SAT, you can combine clauses containing x and (not x), and reduce the problem size overall. But people have proven with 3-SAT, if you try to combine clauses in some tricky way which reduces the number of clauses overall, this DOES have lower-bound exponential time. It's almost like with NP-complete problems, you're stuck with the original problem and it's impossible to reduce, while problems in P can partition the original problem and make it smaller.
Check out Scott Aaronson's P vs NP review paper if you want to ACTUALLY learn the current state-of-the-art for the problem. Pretty much all of it went over my head lol. There's some new approach involving geometric complexity theory, he said it's kinda like string theory, where it's so advanced that it will take multiple mathematicians lifetimes to even begin to explore.