You’re thinking of your “damage” variable there as being two different variables for the purposes of Empowered Spell, that being “d4(casterlevel)” and “1 per casterlevel”. However, my reading based on the example provided by Empowered Spell is that they are all one instance of damage:
If they wanted you to consider the 1d4 and the 1 separately, then they would have worded it along the lines of “roll 1d4 and multiply the result by 1.5 then add 1”. Thus, the spell is considered to have 2-5 damage for the purposes of Empowered Spell, not 1d4 and a separate additional 1, which is congruent to the fact that it is one instance of damage for the purposes of Damage Immunity, Resistance and Reduction.
I believe it is option 1 and that it becomes variable when added to a dice roll, since it becomes part of a random component.
As I stated in my previous post, if Caster Level was considered variable then Magic Missile would shoot more missiles on tabletop due to having a variable amount of missiles based on your level which (on tabletop) influences its number of targets, yet despite it being the example spell of choice for Empowered Spell and thus providing an opportunity to do so, nothing is said about it.
Thus, my conclusion is that “Variable” must mean “Random”, which I think is congruent with the fact that the spell later goes on to say that Empower Spell does nothing to a spell that lacks random components.
I believe there are, as I recall seeing one just the other day while looking over how spell scripts are written while backporting Creeping Cold into Neverwinter Nights 1 for fun. However, to suggest this means they aren’t supposed to be empowered because of this would ignore both the fact that there are probably just as many (if not more, though someone would have to count) scripts that do empower the constant, and the fact that it is unlikely that every spell was written by the same person and thus is subject to differing implementations, either by mistake or even just differing interpretation if Axe_Edge is accurate in saying this is a 23 year old debate.
I would also say your example of Augment Healing being one of these cases is not one to rely on. Ignoring how there could be an entirely different argument about whether Augment Healing would be applied before or after the effects of Metamagic (Based on the wording of the tabletop version of the feat from the Complete Divine book I think it would be applied before), it could also simply be an order of operations error in the scripts that they just didn’t think too hard about when implementing a rather niche feat.