Note that according to that study, in terms of climate impact, the paper bag is better, not worse, than the LDPE bag. It's worse in terms of "total impact", which considers the categories below and I'm not sure how the total score is aggregated -- I'm sure it's explained in detail, the report has 144 pages.
CC Climate change
OD Ozone depletion
HTc Human toxicity, cancer effects
HTnc Human toxicity, non-cancer effects
POF Photochemical ozone formation
IR Ionizing radiation
PM Particulate matter
TA Terrestrial acidification
TE Terrestrial eutrophication
ME Marine eutrophication
FE Freshwater eutrophication
ET Ecosystem toxicity
RDfos Resource depletion, fossil
RD Resource depletion, abiotic
Water Water resource depletion
They also come to the conclusion that it's always better to incinerate paper bags (at end of life) rather than recycling them, which is interesting? If you intend to recycle your paper bag, you need to reuse it 73 times before you do so, because recycling paper is bad (recycling the plastic bag: also bad!). Again, in terms of "total impact"; I think in terms of climate change they say recycling either is good.
And I'm not sure if the paper bags they looked at were themselves made from recycled paper, which they usually are in stores here and which presumably changes the calculation (in either direction). It's odd because they look at like 5 or 6 LDPE variations, including breaking them down as recycled/non-recycled, but I can't find any mention of the paper being recycled or not. Again, 144 pages, maybe I've overlooked it. They do distinguish bleached and non-bleached paper.
Last but not least, they assume you need two paper bags for each LDPE (reference) bag (not enough weight capacity). The same is, hilariously, true for the organic cotton bag (but not the non-organic one!), not because of weight but because of volume constraints. So if they had chosen a slightly smaller -- or larger! -- shopping trip, lots of numbers would go up or down by a factor of two.
I'm not saying the report is bad or anything -- I'm not qualified to say either way --, turns out lifecycle analyses are complicated and full of judgement calls which inevitably get compressed to single statements like the one in the fine article.
Here's the report: https://www2.mst.dk/udgiv/publications/2018/02/978-87-93614-...