Why are 'modern' high-efficiency LEDs easier to damage than 'old' LEDs?

Yes, newer LEDs are also static sensitive. I learned this the hard way when testing a batch of blue SOIC chips with (unknown to me) a soldering iron with defective ground which was later found to be floating at >30V. I can assure you that the LEDs did not work after this experience and it wasn't heat as a single touch to one side of a diode at even 100C ruined it. Some started flashing like demented strobes, some just died completely.

Incidentally newer LEDs based on quantum wells are also highly sensitive to ionizing radiation, I learned this by reading about folks venturing into the ruins at Tchernobyl and Fukushima. The white LEDs in their caving lamps would often begin to flicker and eventually fail, at survivable (for humans) radiation doses. Silicon carbide ones are less so but still eventually fail, rumor has it that Cold War era LED technology is still used today on the ISS Zvezda module and the Progress spacecraft. I did also find that some GaN based blue LEDs can be used as varicaps, in some cases with no effect from brightness loss. The mechanism can generate 100pF changes comparable with an expensive part.