Are paper kitchen towels food-safe?
I will put this as an answer as I might be too long winded for a comment.

The US, and most places have agencies that set food and food handling standards.  I will not get into if those standards are the best, right, too high or low, ect., only state that those standards are when the agencies have deemed qualify as safe.  I will also not comment on how well those standards are followed and enforced, only that they are in place, and should in general be followed.  There purpose is to assure the public that what they eat and what they use to prepare food meets a reasonable health standard.  If, in my opinion, one does not assume that items made within that country and imported by reputable sources into that country do not adhere to those standards, then you will simply worry yourself needlessly over everything.

On this specific question, kitchen towels/paper towels/paper rolls, etc. are specifically manufactured for kitchen and general household use.  They should therefore be manufactured to food grade standards.  Should you simply eat one?  Well no, but it is not going to hurt you if you do.  It is paper and a bit of dye.  As intended for kitchen use, the dye is food grade, not fabric dye or such.  Is bleach used to make it, yes, more than likely since bleach is a common item used to make such paper, but there is not deemed to be enough residual to be a health risk, and certainly not enough to be a contact risk from draining of blotting food.  That does not mean it is recommended to start shredding them up and use them as a food supplement.  It means that board review says causal contact with food is OK.

That does not mean that any paper or cleaning towel is OK to use.  If it has been treated with cleaning or polishing solutions, like disinfection wet towels, those are not for direct contact with food.  It is not their purpose, and yes, they might very well make you sick.

Is plastic safe?  Well, it depends on the plastic.  If it is food grade, then yes, as long as it is used reasonably and as intended.  Take a thin zip lock bag and super heat it, well, that is not how it was intended to be used, and you may well have broken its integrity.  Use it to store a piece of fruit in the refrigerator for a day and it is fine.  Go to the hardware store and get a plastic bucket to mix something in?  NO.  That is not food grade plastic.