You have not read the document that you link. Else, you would have noticed that it states that a not-organic cotton bag has to be reused 52 times for the same relative impact on climate change. The 7100 is impact on ozone depletion:

p. 18: 'Conversely, for composite and cotton the very high number of reuse times is given by the ozone depletion impact alone. Without considering ozone depletion, the number of reuse times ranges from 50 to 1400 for conventional cotton, from 150 to 3800 for organic cotton, and from 0 to 740 for the composite material bag. The highest number is due to the use of water resource, but also to freshwater and terrestrial eutrophication'.

And as I have commented elsewhere: I have cotton bags that I have easily used 500 times. If I had used an old T-shirt for the bag or later use the old bag for cleaning purposes, the 7,100 becomes very relative.

Aren't the plastic bags mainly a problem because they tend to end up in places where they don't belong at all, like oceans etc.? They can't really decompose or anything like that, they just shred to tiny little pieces that mess with animals (and ultimately also our) digestion, no?

Yup. There are places where plastic bags accumulate. Once it was my doorstep. Every morning there were piles of plastic bags that were delivered to my house.

Just take a trip along any river or stream near a town and you’ll find them swimming by like lifeless jellyfish

And microplastics don't just mess with digestion, they're also theorized to be part of the reason fertility is dropping in humans over time.