Maybe bitwarden has a hardcoded list of browsers and defaults to the app id otherwise? There could also be an override, but if not you'd have to open an issue with bitwarden and wait for them to update their list.

Edit:
Looking into the code there is indeed a hardcoded list.
This file contains the code

// Docs state that password fields cannot be reliably saved in Compat mode since they will show as
// masked values.
bool? compatRequest = null;
if (Build.VERSION.SdkInt >= BuildVersionCodes.Q && fillRequest != null)
{
    // Attempt to automatically establish compat request mode on Android 10+
    compatRequest = (fillRequest.Flags | FillRequest.FlagCompatibilityModeRequest) == fillRequest.Flags;
}
var compatBrowser = compatRequest ?? CompatBrowsers.Contains(parser.PackageName);

I read this as:
There are browsers that do "native" autofill and ones that do "compat". Mull and ironfox do compat.
This compat support is communicated on Android 10+, but either on older android or maybe if the app is built for older android (?) it won't be communicated, thus the hard coded list.

Doesn't look like there is a way for users to add to this list.