The Improve-by-level math has been present in all versions of D&D- PF2 just standardized it and applied it across the board.
Skill system- the new system is very much like the old system. In fact, you can makes a case that the old skill system is the math upon which the entire new system in based. Rather than apportion skill points, you automatically gain a skill point in every skill in which you are proficient as you level up. Skill Focus feats and such are replaced by the proficiency levels (trained/expert/master/legend).
Combat system- in the new system, everyone has full BAB in their chosen fields of combat. They also gain in defenses as they go up in level as well. While I'm still evaluating the system as whole, the fact that higher level characters become inherently harder to hit as they gain levels sounds very cinematic and intuitive to me- You shouldn't be able to land an easy blow on a master swordsman. differences in ability are handled by proficiency levels rather than by 1x/0.75x/0.5x multiples
Saves- as in the previous two, differences are handled by proficiency levels. Curiously, in this case, the differences between trained and legend (+6) is exactly the same as between a good save and a poor save in PF1/3e.
the design choice of scaling at 1x is really bold- 4e scaled at 0.5x across 1.5x levels, which still winds up with a slightly lower spread than PF2. But it appears to me that the level-scaling in here is so uniform that you can literally rip it out entirely far, far easier than you could do with 4e.