There are a variety of synonyms that can be used in place of "fade into insignificance." Some of these might include "lose significance," "diminish in importance," "become unimportant," "pale in comparison," or "lose relevance." All of these phrases suggest that something was once important, but has become less so over time. This can happen for a variety of reasons, such as changes in circumstances or new information coming to light. Regardless of the reason, the end result is that the thing in question is no longer as relevant or important as it once was. Using one of these synonyms can help to communicate this shift in meaning.