Reporting that there is a policy is no bug, but maybe there should be a way to signify that it's customized by your software vendor (i.e. signed and keys are compiled in) and that it just sets the default search engine.
Chromium does change the message to "This device is managed by <google workspaces domain>" if attached to Chrome Enterprise.
The policy config is designed for enterprises, not software distributors. It's Debian that's taking an unnecessary shortcut here. They could've patched the source code to change the default search engine.
Chromium does change the message to "This device is managed by <google workspaces domain>" if attached to Chrome Enterprise.