I can help you. Authenticity is a synonym for trust, in the context of elections. Its the core of voting preference. That is, the candidate who wins is the one who the voters best trust to represent them.
Inauthentic candidates are seen as less trustworthy to do so. To varying degree. In other words, they are seen to be liars to varying degree. That is, inauthentic. Now you've caught up on how the American mind works in elections.
In the context of how the Get Trump Witch Hunt, ongoing since 2015, has affected eelections going forward: voters are now prone to see such unusual behavior from the opposition as a marker of candidate authenticity. Such is the nature of democracy poisoning actions.
In other words, if a candidate is not subjected to roughly equal treatment, then they will be widely seen as less authentic (more aligned with the opposing party than someone who is subject to it). This was obviously going to be the case going forward, beginning in 2016-17.
Which is a horrific situation for democracy.
To wit, in January 2024, Trump's RNC opposition have degraded themselves to appeals to the supposed fact that the opposition hates them less and therefore they will be more effective. They largely don't (at least effectively) sell themselves on authentic behavior. Possibly because they lack the actual conviction to sell it. Instead, they are essentially tacking toward inauthencity as their primary sales pitch. As a result, they don't stand a snowflake's chance if voters are the determining factor in a head to head primary.