Error 'Failed to open. Stack unavailable' that appears after clicking the Sign in with browser on the sign-in form usually indicates that your system has no browser set as the default browser.
Setting up the default browser will most likely solve this issue. For that, go to the Start menu, find the Settings app and launch it. On the app, go to Apps → Default apps → scroll down to Web browser and select anyone on the list. Restart TradingView Desktop and sign in.