Precisely this. Earth's 'normal' extinction rate is often thought to be somewhere between 0.1 and 1 species per 10,000 species per 100 years. A mass extinction event is when species vanish much faster than they are replaced. This is usually defined as about 75% of the world's species being lost in a short period of geological time - less than 2.8 million years.

The current rate of extinction is between 100 and 1,000 times higher than the pre-human background rate of extinction. What we're going through will be an extinction event on a timescale and severity that will be closer to the Permian or Cretaceous extinction, which resulted in the species death of 95% and 78% respectively, and caused by apocalyptic scenarios; meteors and volcanos effectively suffocating the planet. Never before has a single species been responsible for such destruction on Earth.

I suspect humanity will survive whatever future is yet to come. I just hope we managed to preserve a substantial percentage of natural diversity through that process.

Yes, but mass extinction is the result of our greater land usage and resource overexploitation, not climate change (in that it would be happening even if climate change was not).

This also makes it harder for many species to adjust to climate change and habitat loss as it is much harder for them to migrate.

Not strictly accurate; it's the major part of it, but climate-change driven species loss is a real threat and at some point will likely outpace the rate of loss due to land/resource exploitation.

Ocean biodiversity loss is almost certainly harmed by overfishing and toxic run-off from rivers/lakes don't get me wrong, but it's also hugely impacted by rising sea temperatures. Ocean biodiversity increases exponentially with sea surface temperature up to about 20-25 C (68-77 F). Beyond that threshold, biodiversity drops off due to the limits of aerobic metabolism. Temperatures that make it hard for cold-blooded sea creatures to breathe have likely been among the biggest drivers for shifts in the distribution of marine biodiversity.

Desertification, caused partly by human agriculture and the removal of soil-retaining plant matter but mostly due to climate change, is also a major cause of species loss and it's occurring across much of the planet - especially Africa and Central Asia. Those animals that can't rapidly migrate to cooler/wetter climates are ripe for extinction.