In the past this has worked in Debian but the versions from Unstable and Trixie don't work. https://www.chromium.org/administrators/linux-quick-start/ Above is the documentation on how it should work.
This might be related to enable_enterprise_companion=false. I disabled it because it included a binary, but that might've been a bit too aggressive. I'm guessing versions 138.x worked for you? If you're willing to test a package, I can come up with a better fixx and upload one to people.d.o/~dilinger/ for you to test out.
Version 138.0.7204.183-1 had exactly the same problem. I tested 139 because reportbug recommended the version in Unstable. Yes I'd like that thanks! There are significant security benefits to a managed environment, it allows controlling things like clipboard which aren't obviously/easily settable by a skilled user and also allows restricting installation of plugins which is necessary when running systems for older relatives.