Literally the frist sentence in the abstract:

More than 50% of the world’s population lives in cities. Its buildings consume more than a third of the energy and generate 40% of the emissions.

"higher densities lead to higher CO2 emissions" you say...

The low density/low height example in the nature article is still 5k people per Km^2. While definitions vary wildly, I usually see 1000-400 people per km^2 for suburb definitions.

Does example D look like suburbs to you? As something undefined it could be considered suburbs, but probably "streetcar suburb" in the Canadian/American context.

Critically the article also mentions a requirement for best practice greenery management to maximize carbon sequestration. I'm no botanist, but I'm guessing caretaken parks do better then monoculture lawns (assumption).

Edit: missed that the first link was a different study. That like on spanish cities has its lowest density group defined as <100 pop/hectare, if my math is right, that means <10,000 pop/km^2. Significantly denser than any suburb. This is also a region when thermal energy is spent of cooling, not heating. And while it adjusts for climate effect, it doesn't seem to adjust for the modernity/thermal effectiveness of the buildings. Such to say, a building with an air-conditioner will spend more thermal energy than one without.

Basically your two links are showing that cities can be too dense, and there is a point when they lose GHg efficiency. There is no mention of anything lower than what, as a Canadian, I would still call high density (just not super high density).

https://coolclimate.org/maps

Feel free to zoom in on essentially every city in America. You can even download the raw data yourself.

Further, your Nature study you link, actually read the paper and you find this nugget:

These limiting assumptions were necessary based upon the urban scale scope of this study. Providing additional levels of detail at the building scale would greatly improve the accuracy of the analysis and can be refined in future works. Employing a cradle-to-cradle approach to consider resource reuse, the impact of retrofitting existing building stock over rebuilding; the inclusion of transportation impacts; adding a dynamic time component to investigate material inflows and outflows; and including a detailed time-related analysis of carbon sequestration potential offered by urban greeneries in the simulated environments—are all valuable and important avenues for future work to build on this study and expand its relevance while reducing its limitations. This study therefore acts as a stepping-stone to provide a strong foundation from which extensive future work can be born.

It literally doesn't even model transportation emissions. Considering this whole conversation is about sprawl causing more cars, this is kinda a glaring omission.

I'd like to come back and read over this later. The point OP is making seems pretty obvious but it is quite directly contradicted by the sources you just provided. I want to read those later