Red dwarfs also subject their planets in the putative habitable zone to much stronger stellar winds and flare radiation, which makes survival of their atmospheres problematic.
It’s a bit like losing your key and looking below the street light because that’s the only place you can see - only that the street is littered with millions of potential keys anyway.
That represents an extremely poor environment to try to evolve life in. The only temperate place would be a ring at the terminator with the sun permanently just above the horizon.
With a very massive moon -- or a double planet, like Pluto/Charon, it might be possible to avoid tidal lock.
With an ocean of liquid water evaporating on the sunlit side and condensing away from it, but flowing back through the ocean (and even rivers), the sunlit area may (theoretically) have relatively a temperate climate, as opposed to being a star-scorched dry desert.
This system is less than 5 parsecs / 16 LY from Sun, which likely makes it one of the systems more amenable to detailed research, as bigger telescopes become available.
My naive model: atmosphere on the warm side goes up, moves with hot humid air toward the cold side, goes down and back to the warm one with cold dry air.
Less naive model: we have three large convection cells here on Earth between the pole and the equator. Maybe they have several cells there too. That could slow down the transfer.
Furthermore dry is never 100% dry and when there is little water left the transfer will slow down. How much water will be left and for how long, I can't say. There could be the equilibrium I'm thinking about or not.
Other variables: volcanoes melt stuff locally, glaciers flow to lower ground, continents move.
Edit: I found this paper about weather on tidally locked planets https://www.pnas.org/doi/10.1073/pnas.1315215111
But without a magnetic field, the only hydrogen is what is locked up in ice or other solids.
The migration of water to the dark side changes the center of mass for the planet, right? Might that be enough, especially if there are any other bodies around to throw in some chaos, to pull the ice back into the warmer region?
At first armies can march in one direction of the ring or the other, with every natural defense point being sort of a Thermopilae situation
Then, technology progresses and certain machines may allow smaller groups to traverse outward for limited periods of time. Analogous to our submarines?
Would then flight make the world "flat" and globalized?
They can't lay cables across the scorching dor icy deserts, so worldwide comm must either follow the ring or be satellite-based
Ocean to the north and desert to the south and only a thin strip in between where to live and wage war in.
"The closeness of the host star to the Sun makes [it possible] for their atmosphere to be studied via high-contrast high-resolution spectroscopy."
Hopefully they can follow-up soon with those measurements. That could bring clarify to your fundamental questions.
[1]: https://en.wikipedia.org/wiki/Hydrothermal_vent_microbial_co...
Realistically if we wanted to look for life on a foreign object, we would probably start with the candidates in the solar system.
1.4 solar masses and yet much dimmer than the Sun
This is not even physically possible unless the star is a post-main sequence white dwarf.