His job was to negotiate transfers and become the bridge between the head coach, scouts and the board. And negotiating transfers and contracts was his job but he didn't identify players to recruit because that was the job of the recruitment department which was led by Dave Fallows and Barry Hunter. That's their field and speciality.
There was a time at Liverpool when some Liverpool fans had started a petition to remove Edwards from his role due to a lack of experience. And that was brought on by the poor way he had handled the Van Dijk deal reportedly, where Soton ended up reporting Liverpool to the FA. And the deal broke down and wasn't resurrected until a future transfer window and some public apologies.
Without Klopp the narrative around Edwards would've been very different right now because before Klopp's arrival, Edwards and his team was a laughing stock among many of their fans.
A structural setup on the football side of the club is very simple. And Liverpool brought in a head coach who had a defined way of playing the game and he took on a hands on approach to both coaching and helping himself by aligning the recruitment process towards helping him succeed on the pitch. This is something that Mourinho and Solskjaer didn't do. So it's not about having contacts, but actually signing players who fit with the way the head coach wants to build and evolve the team going forward on the pitch. So basically they started working together which was a big change from Brendan Rodgers who was said to be constantly at loggerheads with the then transfer committee.
So Liverpool and Michael Edwards went from signing Ricky Lambert, Lallana, Lovren, Markovic etc to signing Mane, Salah, Van Dijk, Robertson. The difference was Klopp had arrived and he had made his mark both on the playing field and the structural side of the football club.