It's not a given that such events are necessary because human population growth has already slowed down and will continue doing so as more of the world becomes developed. Furthermore, technological advancement can increase the number of people the planet can support. So, while there is definitely some population strain, it's far from certain that human overpopulation will result in catastrophe without events like this.

The former. At our current consumption levels/technology, we are obviously above our planet's current carrying capacity.

This is not controversial. We are living on borrowed time - our civilization currently relies on the consumption of non-renewable resources, and the non-sustainable consumption of renewable resources.

Even if this is sustainable for 10, 20, or 100 years, it is not sustainable for longer time horizons.

It's worth pointing out that for developed economies like the US, UK, and Japan, the amount of per capita energy usage is the lowest it has been in decades:

https://d33wubrfki0l68.cloudfront.net/0784d9d63336606d4ca025...

This may be at least in part due to the shifting of energy-intensive industries to countries like China, but it does show that countries can continue to grow their GDP (per capita) while dropping their energy usage per capita, which bodes well for the future.