König, my apologies if I misinformed the community with my experience. I did indeed report that my California drivers license mentioned my nationality -which I thought it did-, but I have no way of verifying it for sure now. I held one for two years, and I did, as a (non-resident) alien, have to wait several months to get my plastic card while they did background checks, and I had a temporary paper which I had to use in the meantime. That much is for sure. The nationality part (I said nothing about it mentioning "immigration status" by the way), I might have confused with my FAA license, which does mention it. So, apologies for that. If someone has held a California driver's license as a non-resident alien around 2000-2002 and wants to confirm that it does not mention the country of nationality, that would be great.
For the rest, I merely related my life experience, and how I was never asked (or told, or read in immigration pamphlets, etc) so specifically to carry my immigration documents with me at all times, nearly as much as it was made obviously clear to carry my GC around in every single document I read once I received it. (that's why I said "I do not recall") I am not trying to contradict the law and I certainly believe that according to every immigration officer, whatever your alien status is, you are supposed to carry everything all the time.
I just read the following paragraph, which relates the experience of an H1-B visa holder who had some issues while traveling in another state and it makes me feel like I am okay to not carry my documents around in my state of residence.
"The CBP officer just told me, “ if you are not US Citizen or permanent resident, legally YOU HAVE to carry your Passport, I-94 and current Immigration Status document (like I-797 for H1B), whenever you are traveling out of your current resident state.”
This forum is intended to share experiences. I make no claims, I am not trying to be right or wrong. I apologize for suggesting anything to the contrary.