All but the most corner-cutty TP manufacturers (hopefully) remove those contaminants during the pulping process (as shown in the video; the video mentions ink and metal/plastic debris specifically, but this is where you'd filter out any other contaminants). If it's a danger to your water supply, then it's probably a danger to your behind, too.
Not sure where you live, but in areas with public sewage of course the treatment plants remove as much as possible from the water before it reaches nature.
That makes it sound as if the feces are just flushed out into nature, which is very far from my understanding.
Of course the purpose of a sewage treatment plant is to remove as much as possible of the material in the water, regardless of what it is, ending up with water that is as pure as possible so it can be let out into nature.
A large part of the US depends on septic systems. After flushing, the water, feces, and toilet paper all end up in a tank on the property. The toilet paper and feces there dissolve into the water thanks to bacterial action and other processes, and then eventually flows into a field line that distributes the water into the soil. This is entirely a passive process that can go decades without maintenance, though newer designs in wetter areas sometimes have a pump that sprays the water on the surface after chlorinating it.
My understanding is that the solids are separated from the liquids and in the case of the MWRD of Chicago [0], air dried before being put to reuse.
The point is TP just becomes part of the solids and there's no need to separate it from the rest of the solids, it's complementary being derived from trees.
"Recycled paper is an important raw material to provide sustainability of natural resources and reduce the environmental impact of the use of paper from recycled pulp in the packaging industry. Hence, recycled paper production is higher in terms of volume and utilization. Recycled paper products are used in the packaging industry partially or fully. Such usage leads to the presence of heavy metals due to recycled and chemical additive sources. The present study aims at determining the amounts and also identifying the sources of heavy metals such as Pb, Cd, Zn, Ni, and Cu contained in recycled testliner (TL) and fluting (FLT), which are main products used in production of corrugated cardboard. The metals in the structure of the paper used in packages directly or indirectly in contact with foods are heavy metals. Mean values of 2.6 mg kg-1 Pb (lead), 2.8 mg kg-1 Zn (zinc), 0.094 mg kg-1 Cd (cadmium), 1.8 mg kg-1 Ni (nickel), and 25.4 mg kg-1 Cu (copper) were detected in test liner and fluting papers using inductively coupled plasma optical emission spectrometry (ICP-OES). The main sources of heavy metals are colorants, mainly consisting of conventional paint and pigments as well as spot and Pantone Matching System (PMS) colorants."
I don't doubt that there are residuals in recycled paper, I'm doubting that they outweigh the downsides of using fresh wood. It just seems like a convenient thing to tell yourself to calm your conscience when buying extra-fluffy TP.