From the transmissions in Pathfinder's logs you learn that Reapers attacked and most likely everyone in the Milky Way is dead, as there hasn't been signs of life since 2186. But doesn't this contradict Mass Effect 3 ending, where no matter which of 3 choices you make, the Milky Way is saved?
IIRC, no matter which ending you choose in ME3, the relay network gets destroyed. The relay network was, among other things, responsible for interstellar communications (apart from the quantuum communication system, which was top secret, bleeding edge stuff in ME2.) So, although life in general was saved, civilization - at an interstellar level - was crippled.
So, from the perspective of the Andromeda team, there wouldn't be any signs of life back in the Milky Way after the Reaper invasion, but that doesn't mean there's no life at all.
Upon reading deeper into some of the logs, and also from certain conversations Ryder has with various NPC's, you learn that the Andromeda Initiative launched well before the events of the original trilogy occurred. Therefore once arrived in the new galaxy some 600+ years later, no one from the initiative would know what the outcome of the Milky Way conflict was.
So to answer the original question, no, it doesn't contradict the ME3 ending(s).
Within the game,
There are conversations on how the Golden worlds were picked. They did an extraordinary amount of research. The Andromeda Initiative chose the world, that each pathfinder would eventually explore and colonize. Once they finally got there, all their research and theories failed.
With saying that. Within the Pathfinder's logs, as you stated in your question.
"There hasn't been signs of life since 2186"
All you know is what's in the logs. It says that there hasn't been signs of life, but how do they actually know. They really don't. More of an observation.