Which browsers
Chrome, Chromium, Edge, Brave, Opera, Vivaldi, and Firefox with LibreWolf and Waterfox, on Windows and Linux. Browsers installed as Flatpak or Snap packages can't reach the app, so they can't pair.
One unlock for app and browser
Pair the browser extension with Vallkey for Windows or Linux, and the extension unlocks whenever the app is unlocked, and locks when it locks.

How it works
In the extension: Account, then Vallkey desktop app, then Pair with the Vallkey app.
The extension and the app, unlocked on the same account, show the same code. Allow the browser in the app.
Open the locked extension while the app is unlocked, and it unlocks. Lock the app, and its browsers lock too.
The details
Chrome, Chromium, Edge, Brave, Opera, Vivaldi, and Firefox with LibreWolf and Waterfox, on Windows and Linux. Browsers installed as Flatpak or Snap packages can't reach the app, so they can't pair.
Browsers, under Account in the app, lists the paired browsers. Forget one there, or stop from the extension's side.
The app unlocks the extension, not the other way round. Your master password still works in the extension.
Safari reaches only the app an extension ships in, so Vallkey for Safari isn't paired.
Availability
Pairing is for the Windows and Linux app. On a Mac, Vallkey for Safari comes with the Mac app itself.
A program running as you could ask the unlocked app for the key the way the extension does, as it could read the unlocked app's memory. No password manager fully protects an infected device, and we'd rather say so.
Vallkey opens soon. Join the waitlist to hear first.