React Native: Deep link handler doesn't fire on Pixel 6

Question

The listener for deep-links successfully registers my handler:
Linking.addEventListener('url', handleUrlDeepLink);

But on Pixel 6 for some reason the handler doesn’t fire when clicking on a deep link.
The app opens up, but nothing happens and no logs appear.

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We use React Native v0.61.5
It's possible that it's fixed in newer versions of React Native (Linking library).
But unfortunately, currently we can't upgrade as it brings other issues.

App.js:

import {Linking} from 'react-native';

const handleUrlDeepLink = url => console.log(url);
Linking.addEventListener('url', handleUrlDeepLink);