While I can't tell for sure the finish is probably an industrial lacquer finish. From the pics it appears that the piece has been in the sun, which has lightened/bleached out some of the original color, and lost some finish from years of use/abuse.
In response to your original question: "How can I add a bit of color and finish to those areas without redoing the whole door" Here's a couple responses from the 'short-term, cheap and easy' to the 'still simple, but better'.
For both methods try to find an area that is some damage, but isn't seen a lot. This can be the side of a cabinet door, the bottom edge, even the inside of a door. Use this as your 'test' area. Whichever method below that you use, test on this area first - then go to the front of the doors
For a cheap, short term "fix" go to a local Lowe's or Home Cheapo and get a product call Howard's Restora-Finish. Use the darkest colored area as your base color from which to work. Howard's comes in a variety of different shades/colors, so buy one that's the same as your base color, one that's a touch darker than your base color, and one that's a touch lighter than the base color. Start with the lightest color, apply according to instructions on the can, and wait a few hours. If it's the right color great. Save the can because you'll have to use it again in a few months. If it's not dark enough apply a 2nd coat of the same color. If right, good. If too light, let sit for a few hours and then apply the next darker color. Again, If right, good. If too light, let sit for a few hours and then apply a second coat of this color. You should be close to the color by now.
A simple but better 'fix' takes a bit more work, money and skill but yields a much better longer term solution. As above Use the darkest colored area as your base color from which to work. You're going to have to but spray cans of lacquer wood toner. You can buy these on Amazon or Ebay - here's an Amazon link https://www.amazon.com/s?k=behlen+lacquer+toner&hvadid=77927938306436&hvbmt=bb&hvdev=c&hvqmt=b&tag=mh0b-20&ref=pd_sl_512twg0hsg_b
Follow the steps as above and on can. Before doing any spraying, light sand all surfaces to be sprayed with a 320 grit paper. Wipe all surfaces with a rag dipped in paint thinner to clean all surfaces and remove sanding dust. Use a vacuum cleaner to remove last traces of dust. Work with good ventilation and eyewear. When spraying a common mistake is applying too much. You want to apply a coat that is just "dusted" on the surface. Don't make the mistake of saying it's too light I have to apply a heavier coat. Let the dust coat dry for about 10 minutes and then repeat. Do this once or twice more and let dry for a few hours. If good, great. If too light, decide whether to use more of this color, or switching to a darker color.