Hey, now. I've made my peace with that being a Kelvin Timeline aberration which thankfully remains well outside the Prime Universe.
Or vice versa, Delta Quadrant ships ending up in the 22nd century Alpha Quadrant. Hell, one alien spaceship of the week on Voyager got reused as the Romulan droneship (described in the episode as a "modified warbird") in the Babel One/United/The Aenar storyline.
You talking about the Vulcan or Romulan everyone thinks is Tamlyn Tomita? Her skin isn't dark enough to be Kima.
A shot done twenty years ago for 4:3 standard definition? Inserting that into a wider screen ratio in high definition would have been a lot more problematic than it would really be worth.
Being set in 2384? Maybe, there seems to be some conflicting information out there at the moment as to when Picard the series is set, though one of the dates being thrown around does make this being 2384 a valid possibility. Being in San Francisco, no, not at all. First of all, if it were in San Francisco, these girls wouldn't be the titular Children of Mars, would they? And when they are outside boarding the school bus shuttle, the sky has a red tint to it, which would heavily imply it should be Mars. And finally, I don't see why an attack on the Utopia Planitia shipyards would trigger an emergency alert at a school on Earth. Mars though, hell yeah.