For me a simple restart of the device did the trick.
I had not restarted my test phone after the update to Android 12 at all. I experienced the same odd bug that a generic app icon was shown in Toasts issued by my app. I tried changing the Manifest as Mickaël‘s answer suggested. No luck. I ended up with the exact same Manifest the app had before I started debugging … and then I restarted the device. My app now displays the correct icon in Toasts reliably. What happened? Unsure. I suspect that a restart may trigger an icon cache refresh that crawls all installed apps in search for new/updated app icons.