TL;DR: This article is misleading and sensational. Do not take it at face value.
The cups were placed in temperate water or sediment and left to leach for up to four weeks.
This isn't how the cups were intended to be used. Yes this can be used to model a threat caused by cups littered into our environment; but this article tries to spin this out first to scare you.
Coffee cups are made of a complex mixture of synthetic materials and chemicals. Manufacturers add processing aids, heat stabilizers, and other substances, many of which are known to be toxic. Even if plant-derived materials are used—such as polylactic acid, a material derived from corn, cassava, or sugarcane that’s used to coat paper cups—cup makers often add a number of other chemicals during processing.
More scare tactic information; preying on your lack of familiarity with how these things are regulated or tested. Scaremongering continues for two more paragraphs before it abruptly changes tone midway.
Improving recycling practices would be a logical step in trying to keep harmful chemicals from ending up in nature, but researchers say it’s best to retire disposable paper cups altogether. It’s difficult for most recycling centers to separate the plastic coating from the cup’s paper. In the UK, for instance, a mere handful of recycling centers take paper cups. Many coffee shops will collect them for recycling—but having to drop paper cups off takes the convenience out of a single-use product. Today, only four out of every 100 paper cups are recycled in the UK.
By now the author hopes you're scared enough to do as they ask; but if you weren't convinced; they threw in some other statistics at the end, and even breaks their suggestion by showing how inconvenient and impractical it is to recycle them.
In 2019, a research group from India filled paper cups with hot water to see if plastic particles or chemicals were released. “What came as a surprise to us was the number of microplastic particles that leached into the hot water within 15 minutes,”
They're still not done scaring you though.
On average, there were 25,000 particles per 100 ml cup. The researchers also found traces of harmful chemicals and heavy metals in the water and plastic lining, respectively.
They dump some number of particles on you; giving you zero context, and zero information about how dangerous that is. They only mention in passing the "harmful chemicals and heavy metals", giving no specific concentrations nor giving you any clues as to how much of it is in there.
https://www.sciencedirect.com/science/article/abs/pii/S0304389420321087
Unfortunately the above article is pay-walled; and is difficult to access. I doubt the journalists read the full paper. Everything mentioned in the article is accessible from snippets on this exact webpage; which may mean things are being taken out of context.