Great question, I glad you asked. When I said both multicellular and microbial life would be fine, what I meant is it's unlikely either would be wiped totally out.

As highlighted in the article you linked, only about 90% of [multicellular] species died out during the Permian-Triassic Extinction Event, specifically the "things have been worse before" situation I was thinking about. Also noted in the article is that the conditions we're experiencing now are not to the same degree although we're observing events similar to what we understand may have happened during the Permian-Triassic Extinction, again to a much lesser degree.

Keep in mind atmospheric CO2 levels were estimated to be around 2500 ppm, about 6 times greater than our current levels of around 420 ppm. Preindustrial CO2 levels were 270 ppm, so we've added about 150 ppm. It's not all that much but it's enough to start changing things for the worse for many of the planet's current inhabitants.

As to microbial life, I'm a microbiologist so I know my microbes. They as a whole are far more resilient and will outlast all multicellular life. Some thrive in conditions where no multicellular life on Earth could survive. Even if conditions were so hostile than no microbes could survive, some form endospores. These are incredibly resilient little escape pods that can remain viable for millions of years, then reactivate when conditions are better, reconstituting back to bacteria.

While extinctions are frankly depressing, they do open ecological niches into which other species with suitable traits can expand and, given time and selective pressure, differentiate. For example, all we'd need is mice and a suitable food source to survive and, a few million years later, the earth will be covered with various species decended from both of them.