As far as we know, that’s correct and L1 unlimited doesn’t exist aside from a few odd exceptions (the starters, legend cards, and also apparently the Prime cards that surfaced on twitter)
One other note: At this point I’d be skeptical of any new unlimited L1 cards that appear. At least one example has been proven to be 1st edition with the stamp acetoned off
Here’s a thread with more info: Unlimited L1 Legend cards?