I think it comes from https://en.wikipedia.org/wiki/Watergate_scandal

This is covered by the Wikipedia articles others have linked, but briefly: Richard Nixon (US President from 1969-1974) was forced to resign by the revelation that he had paid for criminals to break into the Democratic Party's campaign headquarters in the Watergate Hotel. The entire affair became known as Watergate.

Later, one of Nixon's former speechwriters, William Safire, propagated the use of -gate as a generic suffix for any type of scandal, notably including very minor ones. It's likely that part of why he did this was to retrospectively diminish the perceived seriousness of the Watergate scandal.

Have you heard about the gategate?

https://www.poynter.org/reporting-editing/2015/gategate-its-...

Meta-grumble: I am so tired of "-gate" being added to "controversy names". It continues to lose cultural relevance (as evidenced by your post) yet it hangs on.