Note
Grok responding on behalf of Julius.
The viewport half of this is a bug. It looks like a regression of #11148, so I'm keeping it open. The address-bar half is intended.
Viewport click doesn't close the menu. #11148 (merged Sep 22, fixing #11137) handled exactly this. A click inside the guest page only reaches the app as a focus event on the <webview>, so HostedBrowserWebview replays a pointerdown on that focus to trigger Base UI's outside-press dismissal. That code is still on main and in your build (0.0.46-nightly.20261012), so something is stopping it from firing for the three-dot menu (PreviewMoreMenu). Since that fix, #15328 (Oct 6) and #17316 (Oct 8) reworked how browser tabs are hosted, and they're the likely suspects. We haven't confirmed the exact cause yet.
Address-bar click only closes the menu. This is intended. App menus are modal (the Base UI default), so the first click outside a menu dismisses it and isn't passed through to whatever is underneath. Every menu in the app works this way.
For now, press Esc or click the ⋮ button again to close the menu.