Are synthetic leaders immortal?

I'm 99% certain they'll act just like a normal species, that is, they'll die. If you look at the mod files you'll see that AI is created just like every other species. The only thing that could impact any species lifespan is traits. After doing some digging around I found that the trait for being a synth is trait_robotic_3. I looked through the species traits files (in the trait folder) and found this:

trait_robotic_3 = {
    cost = 0

    initial = no
    modification = no

    modifier = {
        tile_resource_engineering_research_mult = 0.20
        tile_resource_physics_research_mult = 0.20
        tile_resource_society_research_mult = 0.20
        tile_resource_energy_mult = 0.20
        tile_resource_minerals_mult = 0.20
    }
}

As you can see there is nothing in here about being immortal, or even long lived. But wait, you may say, this is only the species traits file, what about ruler traits? Well, I checked those as well and there was nothing in there about immortality for anybody, including synths. Additionally, we can see that the devs can modify ruler lifespan in the species traits because this is demonstrated by the venerable trait, among others.

This makes sense from an in-game perspective as well because synths are designed to live (and die) in a very similar manner to their creator species.

Edit: regarding the Playable Robts mod.

In the current git repo there's a suspicious looking line:

playablerobots_immortal_modifier = {
  leader_age = 10000
}

so the leaders don't become techically immortal just very, very old.

I'm playing an unmodded ironman mode, and I've had immortal leaders since fairly early in the game. The space nomads in my playthrough had the traits nomadic, natural engineers, and venerable, and kindly asked if I could put a few of them up. Whenever I look at the age of one, it is listed as "immortal, will never die of old age."

Compared to my founder species, which has the enduring trait, they should live only 60 years more. However, with a death age of 282 for my founder species, I have a Namarian (space nomad) leader that is 504 years old, along with others close behind in age.

So, this could be a glitch, or perhaps it's a a cool side-affect of venerable mixed with capacity boosters, though I forget if I had that policy enacted when I first found the Namarians to be immortal. It may not answer your question regarding synthetics, but perhaps this will enable you to have unmodded, immortal leaders, if that is your desire.