You can enable it on the stable channel, however it is currently hidden behind the flag menu.
The new fingerprint-protected Incognito tabs feature for Chrome for Android is a lot of fun. 9to5 Although you still need to delve deep into the settings to enable it, Google found the capability in the Chrome 105 stable channel.
Enter “chrome:/flags/#incognito-reauthentication-for-android” into the address bar to provide a little extra security to your private browsing sessions. The option to “Lock Incognito tabs when you exit Chrome” should appear after enabling the flag and restarting Chrome. When you exit an Incognito session and re-enter it, your tabs will be replaced by a “unlock Incognito” screen, and you will be prompted to scan your fingerprint.
Since a few years ago, Chrome on iOS has had an Incognito mode supported by biometrics called “Privacy Screen.” However, this is a first for Android. Although this isn’t sure to become a generally available user feature because Chrome’s “flags” menu is technically for tests and in-development features, the fact that it has made it to the stable channel and is compatible with iOS is a positive omen.