I further explored my options: a complete wipe / fresh install of One Drive didn't change anything. The CPU usage was as high as before.
So I moved 90% of my files to iCloud Drive, and after syncing settled (it took OD a day or so to figure out what just happened) the app seems to finally behave again - the first time in months.
I'll probably move the rest, too, and just leave the company data in OneDrive. It has been way too much trouble since the beginning of this year. During this time there was zero support, bad design decisions and misbehaving versions of the app – preview or not.
I'd excuse them in an instant if it was the friendly garage-based startup, with great intentions but too many balls in the air. But it's the biggest software company in the world, for Chrissake. And the rosy blog posts about a so called new experience couldn't be more disconnected from my reality, or many others' here.