Oh. Hmm.. Well I suppose that could explain why everything in Andromeda isn't thousands of years more developed than the Milky Way races, but on the other hand it could've been interesting to bump into at least one race that was that advanced.
It isn't stated they are constrained to the MW, but it doesn't mean they aren't. It wouldn't even be ret-conning
1) I doubt the Reapers, or Leviathan would reveal the finer points of their programming in the 20 mn conversation they both had with Shepard, who was only interested in the fate of the MW anyway. That would have been irrelevant to the conversation. imagine this:
The Leviathan:
"To solve this problem, we created an intelligence with the mandate to preserve life at any cost."
"The intelligence has one purpose: preservation of life"
"But don't worry, we didn't forget to preclude any other galaxy from their programming, so you could, you know, flee there instead of fighting them? Damn! Wished we'd remembered to preclude ourselves from any stupid preservation attempt..."
The Catalyst:
"Without us to stop it, synthetics would destroy all organics"
"Organics create synthetics to improve their own existence, but those improvements have limits. To exceed those limits, synthetics must be allowed to evolve. They must by definition surpass their creators. The result is conflict, destruction, chaos. It is inevitable. Reapers harvest all life. Organic and synthetic, preserving them before they are forever lost to this conflict."
"By the way, we are constrained to the MW, so we have no idea how our current problem has been handled in other galaxies, and that's why RGB is inevitable for you. So now, what's your choice? Do you want cookies to make it sweeter?"
2) At the cost of repeating myself. Assuming they actually went to Andromeda, it doesn't mean they were able to invade it and establish a new cycle. Reapers don't have wormhole tech. Assuming again they can FTL all the way there, they would all need to move there for a first invasion. Andromeda is bigger, has more stars and possible habitable worlds than the MW, and they don't have the advantage of controlling the resident civilisations there. So that means a large scale invasion like our own Reaper war. Such invasion could only be successful if the local species are too less advanced to fight back. But we know the Remnants were super-advanced. They might have well beaten the Reapers so badly that their survivors fled back to the MW and realized that losing too many of them was actually contradictory to their mandate. However, that opens the question of why didn't the Remnants chase the Reapers here and finish them off? If the Reapers can use FTL between two galaxies, chances are the Remnants can too. Maybe they were lazy.
However, I'm pretty sure they have the same discharge limitations than our ships, they just maybe don't have to discharge as often since their engine are more efficient. Without this limitation, invading the Milky way wouldn't have taken them so long, I would think.
If they can't FTL their first travel to Andromeda, it would mean they leave the MW alone during at least 2 500 000 years with relativistic near-light speed travel, which far exceeds their average 500 000 years cycle. And this is assuming they have the tech to build intergalactic mass relays to cut off the return time. Otherwise we're looking at a 5 000 000 years of complete freedom for the MW. They would violate their mandate just by not being there to harvest the MW civilisations flourishing during their absence.
Maybe the Reapers went to Andromeda, maybe they didn't. We can find as many reasons for their presence or their absence in the next game. We don't know the reason of the Remnants disappearance, anything other than the Reapers could have caused it. So far we don't have any evidence to affirm anything.