Is the fingernail paint designed to discourage people from biting their nails still available? might be worth a try? It certainly would be simple enough to paint onto any vulnerable plastic and maybe it works on rat taste buds too.
Rats (in common with other mammals) avoid capsaicin (the substance that makes hot chili peppers hot). Chickens (in common with other birds) lack the pain receptors that make capsaicin unpleasant and therefore are fine with it in their environment and in their feed.
A common practice is to put hot pepper in bird feed to deter squirrels, and you can also add it into chicken feed to deter mice and rats.
Some believe that rodents are particularly sensitive to capsaicin versus other mammals, but I have not found a good source to support that.
What seems to be the case though is that the way they explore the world with their nose and their frequent grooming behavior means that it is very distressing for them to come across it or walk on it.
I think it is worth finding a bulk bag of cayenne pepper (the hottest that doesn’t fall in the category of super expensive specialty hot peppers), and scattering it on the ground in the area outside the chicken door. I think you have mentioned Asian markets in the area - that should be a good place to get a 2-3lb bag.
Capsaicin sprays are commercially available as pest deterrents and chili oil painted on the door would likely also work, but both would be more expensive than bulk buying cayenne powder.
Bitter apple (which I believe is the ingredient in the nail polish to deter nail biting) is also generally disliked by rodents but more variably (and I imagine more expensively). It too is available as a spray to deter pets from chewing on things.
Remember to wear gloves!
I didn’t do an extensive search for sources as the sensitivity and use as rodent deterrent is a long-known fact that has been supported by scientific research but not really a ‘hot’ (sorry) research topic, but here are a couple if anyone is interested.
https://www.sciencedirect.com/science/article/pii/S0092867402006372
https://pubmed.ncbi.nlm.nih.gov/12974352/
Tax: after a week of practicing, Mr. Chips seems to have mastered crowing.