I've written two parts of a fanfic trilogy so far that speculates about the post-Synthesis galaxy and the way I interpreted it is that the 'Crucible Event' used the mass relays to seed every intelligent lifeform in the galaxy-- organic and synthetic-- with nano-technology.
In organics those 'seeds' combined and multiplied and over time altered us first at a micro (genetic) and then macro (anatomical) level, basically turning us into cyborgs with the ability to send and receive thoughts & feelings via specialized EM/radio emissions, like how geth can communicate wirelessly.
In synthetics, the nano-seeds combined and multiplied to form physical data media that wrote and installed adaptive "software patches," giving sufficiently advanced systems "full AI" capability and protection against reprogramming, making them autonomous individuals.
As organics start broadcasting their feelings the effects are two-fold: other organics experience a kind of cybernetic empathy. Whatever you make me feel through our interactions-- whether it's fear, or anger, or happiness-- you feel it too, and because (almost) nobody actually likes to feel hurt, or sad, or angry, people start treating each other the way they'd like to be treated. They become more open-minded and open-hearted to each other and society benefits from more compassion (even if it was "forced" on everybody). Meanwhile, synthetics receive those signals too and start to 'learn' our feelings and how we think, gaining their sought-after "understanding" of us, and because it's happening in a society where people are motivated to be good to each other, synthetics start absorbing that too.
The Reapers, meanwhile, bug out initially. The Catalyst's last command to them is basically "stop harvesting, the Cycle is ended, leave them to achieve their own fate." The first emotional signals they pick up from organics are terror and anger and hate, and it kinda hurts them, so they take off and once out in space, without the Catalyst controlling them, the gestalt 'racial consciousness' of the species harvested to create each one starts to emerge and realize what they've become, and they decide amongst themselves to commit suicide by flying into the black hole at the galactic core.
But in the continuity I've written, organics (not gonna say who, exactly) reach a point where they think the Reapers could be useful in rebuilding the galaxy so they go out and intercept them, and invite them back, saying, essentially, "it won't be perfect overnight but help us, make amends, and in time there may be forgiveness." Not all, but many decide to pursue a kind of redemption by serving the emerging new galactic civilization. They share their collective knowledge, they re-build the relays, and gradually we learn to communicate with them, too, in a way that each side can understand.
And farther into the future, the ability to communicate mentally by 'radio' and then by touch leads to more direct interface with machines, hybrid intelligences, and conscious control over our own physical bodies, and ultimately the ability to project our minds across compatible technological networks, similar to how geth can upload and download their programs between platforms, and then we become beings of thought able to exist beyond the bodies we're born in.