"It's an environment like nothing I've ever seen," said Democratic nominee Gretchen Whitmer, a former legislative leader, who has held an edge in state public opinion surveys.
I think "held an edge" here means "had an edge". The last part is saying that the former legislative leader took the lead in state public opinion surveys.
But I'm not quite sure if my understanding is correct because I've never seen the phrase "hold an edge".
The full source.
To hold means "to maintain" or "to remain constant (in something) over time".
An edge in the context of opinion surveys refers to a marginal lead versus the opposing candidate(s).
So she has maintained a marginal lead in those opinion surveys. She has been leading by a narrow margin.
To take the lead in the context of an opinion survey means to move from a second or lower position into the top position.
There are a number of related idiomatic expressions:
To edge out / edge in
To have an edge on
A knife-edge (margin, lead, profit, etc.)
In this context the meaning is that the democrat has a slight lead in the polls, metaphorically as thin as the edge of the blade of a knife.
Written differently, it could imply she managed to work her way into the lead through some gap in her opponent's electorate or strategy.
The Democratic nominee edged out her opponent in the polls with a message that appealed to the core values of the party.
Metaphorically this is like taking a knife or some similar thin object, and using it to wedge open something.
