Chrome - unprompted auto-download of files after opening the browser - bug or something else?
First of all, I would recommend running a scan with Lookout just in case it is a virus that is initiating these downloads (I do see you've used Kaspersky so it should be fine if it didn't sound any alarms). However, it's likely a glitch with the Download Manager; I've been getting random redownloads of files that I've downloaded before through Chrome as well. A reinstall of Chrome and clearing the cache of the Files app may help, as well as a restart of the Android device.

Just the other day my Download Manager decided to "redownload" everything in my Downloads folder, yet it didn't download them in the sense that it retook them from the Internet. I think it was just reloading the files because there were no duplicates. It's likely nothing you need to worry about.