A panicked network anchor went home and deleted his entire personal Gmail account. A Democratic senator began rethinking the virtues of a flip phone. And a former national security official gave silent thanks that he is now living on the West Coast. The digital queasiness has settled heavily on the nation’s capital and its secretive political combatants this week as yet another victim, former Secretary of State Colin L. Powell, fell prey to the embarrassment of seeing his personal musings distributed on the internet and highlighted in news reports. The messages exposed this week revealed that Mr. Powell considered Donald J. Trump a “national disgrace,” Hillary Clinton “greedy” and former Vice President Dick Cheney an “idiot.”