If you read that chart, it says they should not have green potato peels. It does not say they should not have potatoes. It does not say they should not have potato peels. It says they should not have GREEN potato peels. That’s often misquoted on this forum. So read the chart and pay attention to what you read.
Also, practically anything you or they eat contains something that can be bad for them or you. An example I’ll use is cabbage. Cabbage is a great food for them and you, but it contains something that can mess with the thyroid, yours and theirs. For it to mess with yours, you would need to eat a few pounds of cabbage every day for a few weeks. Your chickens are smaller so they would not have to eat as much, but they can’t eat as much as you can. So dosage is very important. Also, some of the damage is gradual. They would have to eat the same thing for a while for it to do damage, sometimes a really long time. Usually their bodies will repair minor damage over time. One bite won’t kill them unless it is highly toxic. The take-away from this is to not feed them huge quantities of anything, good or bad, as a constant diet. Give them a variety or space it out.
Another example on dosage is that apple and pear seeds, plum and peach pits, about any fruit seed contains cyanide. But the amount of cyanide is tiny. They would have to eat a huge quantity for it to cause any damage and that is not going to happen. If you make apple sauce or jelly and have a huge pile of mostly seeds, it’s a reasonable precaution to not pile them up for them, though Mom used to throw out huge piles where the chickens could get to them and it never caused a problem.
Something else that often causes confusion on here. Tomato, pepper, and potato plants contain a chemical (the same in green potato peels) that can harm chickens. The fruit does not. Mine love tomatoes, peppers, and potato peels. So give them your excess peppers and tomatoes. But as Kelsie said, don’t toss the plant in there. That chemical causes the plant to taste extremely bitter so they are likely to take one bite and quit. One bite won’t hurt them. Many people allow their chickens to forage in the garden after harvest is over. They often have tomato or pepper plants in there. After one or two bites, the chickens know to leave the plant alone and eat the fruit, but it’s a reasonable precaution to not throw the plant into a run where they are confined.
The kinds of stuff I give my chickens from the garden (excess or waste) include
Cabbage, kale, chard, broccoli leaves, cauliflower leaves, any greens from that family.
Winter and summer squash, cucumbers, cantaloupe, basically any member of the cucurbit family. I just break it open for them. Sometimes they just eat the seeds but sometimes they eat everything except the skin.
Tomatoes and peppers, especially ripe colored ones.
Any salad greens that you can eat. Lettuce, spinach, mesclun, and beet tops for example.
Bits of corn or bad corn I don’t eat. I break off the damaged tips of ears of corn for them. Some ears are not worth my harvesting them, usually from worm damage. I also collect the corn ear worms and feed those to them.
A favorite of mine are the skins from cooked beets. But beware. If they eat them, their poop is going to be red. If you don’t remember you fed them beets, you’ll think they are pooping blood. That got me once for a couple of minutes before I realized what was going on.
I’ll admit I violate what I said about feeding them a whole lot at one time. I’ll often throw a bunch of stuff in there. They attack it and eat a bunch, then quit. They seem to know when they have had enough. But I do not put large quantities of the same stuff in day after day after day. I give mine time to clean their systems out before they get another large dose.
There are all kinds of good stuff in your garden for them. They will get vitamins, minerals, all kinds of good nutrients. Your egg yolks will probably be darker so don’t be surprised by that. Just try to not give them a steady diet of the same thing day after day after day, probably a lot like you eat the stuff from your garden.