killall chromium-browser: no process found
Focus on achieving your goal, not on fixing the specific tool. If you're trying to kill Chromium's tab processes but not the main process, start by comparing their command lines, e.g. using ps -efww or pgrep -alf chromium.
You'll see that all "child" processes have a parameter like --type=zygote or --type=renderer. Since this directly describes the process' purpose, it will be more reliable than relying on minor differences in the executable name (which has nothing to do it as all Chromium subprocesses are named the same; the fact that "chromium-browser" used to work was just an artifact of Ubuntu's packaging).
Since this is part of the command line, you'll have to use pkill -f to match it:
pkill -f -- "--type=renderer"
pkill -f -- "chromium --type=renderer"
You can often times achieve exactly what was requested here by using the <SHIFT>-<ESC> Task Manager in Chrome/Chromium. This gives you an easy way to see which tabs are behaving badly and killing them individually with the End process button.
That's nice, but sometimes you just need to take charge of things from the Linux command-line...
Being able to kill browser processes seems to be a fundamental requirement of maintaining a stable Linux system. Unfortunately, the methods that work for this seem to be continually evolving. It's a battle of wills, I guess.
I haven't figured out what's wrong with killall, which I previously used for this.
pkill is funny. Despite being produced by tab completion, pkill chromium-browser has no effect (just quietly returns an error status). But leave off the trailing r and you're in business. pkill chromium-browse. I'm not sure it does exactly what you want, but at least it does something. I also found that running the command more than once makes a difference.
One clue is that ps -e also displays the shortened version of the name: chromium-browse
...And as noted by the OP in a comment to another answer, this command seems to work well (at the moment) for killing all tabs without killing windows.
pkill -f -- "chromium-browser --type=renderer"