I'm playing the game for the first time and decided to use energy weapons and especially my old favourite from FO3, the Laser Rifle.

I found one and upgraded it with a beam splitter, but I'm now unsure whether that was a mistake or not. While it does more damage, the damage is split between 3 beams so I'm assuming it gets reduced 3x as much by DT, which I expect would make it pretty ineffective against well armored targets. Is that correct or am I missing something?

I think it is only two beams, but either way you are correct the DT is applied against each beam individually. Same deal with the LAER it gets split beams when upgraded but Elijiah's LAER stays as a single beam so it is much better.

It is still a good thing to install as an extra 30% damage makes a big difference. You just need to use something else for high DT targets like a gauss rifle, plasma caster (not the Smitty Special), pew pew, plasma defender or Elijiah's advanced LAER. Fortunately there are not that many high DT enemies out there. 90%+ of the enemies you face have little to no DT so the fully modded laser rifle is a regular workhorse, I always bring mine along even on VH it still drops deathclaws, just needs a few more shots.

I think that (I am very unsure, so don't take my word for it) each of the beams also has it's own chance to crit.

So if both go off, you're looking at 2x crit damage. Which makes sneak attacks very powerful.