This is certainly true for smaller red dwarf stars, however there are other predictions that claim that it is not as big a problem as the more dire predictions would lead us to believe (never mind that there is a growing database of exoplanets orbiting red dwarfs that have low densities indicating that they have held onto their atmospheres and volatiles). More data is needed... which is why the linked paper (and other sources) refer to potential habitability.

That being said, TOI-700 is a larger and less active M2.5V red dwarf that would not have the same level of activity as smaller red dwarfs. Again, TOI-700e is potentially habitable and is a perfect target for future studies about the limits of planetary habitability.

For TOI-700, we know the properties of the star, the radii of the planets and the characteristics of their orbits. My quick assessment is based on the same info for Venus and Mars in our solar system.

Not good and zero. Mars, with an 1.52 AU orbit, is just within the 1.70 AU outer limits of the habitable zone as defined by the "maximum greenhouse" limit. But its mass is too small to hold onto an atmosphere and sustain the geologic activity support the carbonate-silicate cycle that acts as a thermostat on rocky planets. Studies suggest that a planet needs to be twice the mass of Mars to do that. The inner edge of the conservatively defined habitable zone is 0.97 AU. Venus, with an 0.72 AU orbit, is too close to the Sun to be habitable by this definition (contrary to claims frequently found in the popular press).

> it's in the habitable zone of a red dwarf star (so it'll be tidally locked)

So? Taken directly from the linked article: "Increasingly detailed climate modeling over the last quarter century has shown that synchronous rotation is not the impediment to global habitability as it was once thought. In fact, it has been predicted that slow or synchronous rotation can actually result in an increase of the Seff corresponding to the inner edge of the HZ owing to feedback mechanisms which result in the formation of a reflective cloud layer on the perpetually daylit side of the planet."

> it is around the same diameter as the Earth, slightly more massive

No, according to the linked article the mass of TOI-700e is unknown. But, according to the linked article: "based on a statistical analysis by Chen & Kipping of the mass-radius relationship for exoplanets with known radii and masses, the estimated mass of TOI-700e is about 0.85 +0.67/-0.34 times that of the Earth"

So the most probable mass of TOI-700e is 0.85 times that of the Earth (not "slightly more massive" as you claim).

> it is pretty much on the very inner edge of the habitable zone

So? According to one of the references used in the linked article and by the discovery team of TOI-700e (R. K. Kopparapu et al. 2013), the inner edge of the habitable zone for the Sun is at about 0.97 AU. Earth, at a distance of 1.00 AU, is right at the inner edge of the habitable zone and is still habitable.

What are you talking about? The primary mirror on Hubble has a diameter of 2.4 meters while the Habitable Worlds Observatory will have a diameter of 6.5 meters. This is the same size as Webb but operates at much shorter UV and visible wavelengths yielding superior resolution (with a range of technical advances required over Webb which operates primarily at longer IR wavelengths).

> Did those stages fall uncontrollably or was there a de-orbit burn?

I did a bit of digging and found that a total of six S-IV stages launched by NASA using the Saturn I in 1964 and 1965 were left to make uncontrolled reentries (each with a mass of about 10 tons including attached payloads). Likewise, the S-IVB stages from the Apollo 5, 6, and 7 missions were left in orbit to make uncontrolled reentries (with masses of 10 tons or even more when residual propellant loads are included).

After that, NASA made sure to safely dispose of the spent Saturn S-IVB stages because of the hazards of uncontrolled reentries. For the three manned Skylab missions as well as ASTP, changes were made to the S-IVB plumbing and operation procedures to deorbit the spent S-IVB stages over the Pacific to minimize the risk of falling debris.

> Even then, are the Chinese really contempt to be compared to USA in the 70s?

Despite the fact NASA was fully aware by 1973 of the hazards of the uncontrolled reentry of large stages (which is why they started controlled deorbiting spent S-IVB stages in 1973), it was deemed not worth the expense and effort to modify the S-II second stage of the Saturn V to safely deorbit the spent stage for a one-off launch of the Skylab station. NASA decided to accept the known risks... just as the Chinese have decided to accept the risks of uncontrolled reentries of the LM-5B core stage today.