Why is Chrome aggressively consuming CPU cycles? I literally have 0 tabs open, and yet Chrome is consuming a very significant amount of CPU resources, and quickly draining my battery...

Why?
Why - because it's got a bug or loop and can't tell you it's stuck in human terms.

So, you'll need to look at the guts of the program or get someone to help get to why in your case the software wants to eat all your battery.

In activity monitor, first select chrome and run System Diagnostics.... Then go make a cup of tea. When you get back, click Sample Process while you highlighted the selected chrome item and look over the sample results. 



Based on where it spends time, you’ll need to triage things. I recommend people start by filtering the sample as Percent of Thread so you can see where the busy parts of the code are and hide the fames the drop from a high percentage of time to a low percentage of time.



The alternative, is just triage and remove things chrome could do. Pitch all extensions - add them back half by half until you identify the culprit(s).


Catalina: After some hours various things start to crash and/or stop working


Also, keep track of your time spent baby sitting that browser to protect your battery charge. At some point, you’ll know to delete it and import your bookmarks into another browser.

From your detail already in the question, I have high confidence you’ll determine one bad plug in or just remove and reinstall it will quiet it down. That amount of CPU use is egregious and should be easy to chase down. Worst case you have the sysdiagnose that captures more data to analyze.