Long story short, Atom does not correctly handle defaulting to gio (which appears to be what Solus uses), and instead just errors. Electron v3 does switch to gio as default, but Atom have no yet updated to Electron v3.
The fix right now is to set an environment variable:
By setting this in my bashrc file it makes the issue go away, but it's not an easy bug to track down, and the Atom error message (about gvfs-trash) isn't useful.
If possible, we could add to the startup scripts for Atom in the Solus package that they set that environment variable until Atom upgrades to electron v3 since right now this should be affecting ALL atom users since gvfs-trash was dropped from Solus.