Open the shared image, edit, save. The other side gets the save.
Images in the shared folder open like local files. A large TIFF or PSD streams the parts the editor reads, so opening is quick even when the file is heavy. Save, and the changed content syncs to the other computer.
GIMP is one of the editors in KeibiDrop's test battery. Its save pattern (truncate and rewrite in place, preceded by a burst of probe opens) converges in both directions, and the probe opens do not generate false updates. Edit XCF or exported formats on the mount as you would locally.
Editors that save through a temporary file and a rename, the common pattern in Photoshop-style applications, use the save shape KeibiDrop's tests cover most heavily. Export-to-file workflows are plain file writes and sync as such. If an editor of yours misbehaves on the mount, report it; the save pattern name from its documentation helps.
Retoucher and reviewer on two machines: one edits and saves, the other opens the same file and sees the result. Take turns per file. Two people saving the same image at the same moment produces one conflict file holding the losing version, on both machines, so a race never destroys an edit.
For camera dumps and very large shoots, remember the on-demand rule: browsing thumbnails reads only what the viewer renders, not the whole archive. The full frames cross when opened.