Sadly, I doubt there's a good way to do it. Base game envoys don't even have a trait system, adding one would a huge job, and probably require a lot of hacky interface solutions run through edicts and events. The result wouldn't look very good, and it would likely be very failure-prone and hard to balance given the amount of scripting patches it would take to have an effect.

^What he said^

In stellaris envoys aren't people.

I doubt they'll ever have much more personality behind them than a picture of your pops on a colony ship, unless PI themselves get involved.

The fact that there's a picture that we recognise as an object doesn't mean that there's something behind it that the game recognises as one.
Did you notice that envoys:
-are not hired
-can not be fired
-can not be manually replaced
-do not have levels
-do not have any traits

I'm actually not even sure if they can die (including death from age since I play with enormous lifespans on my core species venerable, necrophages, lithoids, usually more than one source and then techs/traditions for more of it before the time I bought with traits runs out)

AFAIK all the data they have are name, species (so that the game can match a pic to them), current assignment and assignment-switching CD timer.

Did I miss anything?

Judging from the mods I've seen there isn't an easy way (if any at all) to make stellaris reference new types of data. This one, for example, relies on traits to store character data (as far as I can tell).
Envoys don't have any such data to use.
You'd need custom arrays (stored else-where like in an dummy empire-wide effect) that are not actually directly linked with any envoys and then hack-job that custom data into envoy activities of which there are many types.
You'd need to "hack" into diplomacy, into espionage, and into 1st encounters and find ways to affect those based on that custom data with nothing but envoy's id to work with and link it to.

Sounds like a metric ♥♥♥♥♥♥♥ of work for an iffy result and that's at best.

Or at least that's my guesstimate, I'm in no way an expert.

On the other hand it shouldn't be too hard to create a mod that emulates "envoy corps" - a unified dis-personalised "diplomatic" institute that gives the same bonuses to all your envoys and develops in an rpg-like fashion. But that'd be about developing your diplomatic tools techs tricks and methods not the envoys themselves.

Like I said - In stellaris envoys aren't people.

I've had an envoy die on mission to make first contact, but yeah that explains it. I didn't know envoys literally had nothing to them aside from age and race.

Selectable envoys and different traits would be cool. But i would be carefull with percentages of modifiers. Just a little bit of variety that supports specializing of a type of playstyle which would be an incentive using it in the first place.