Thanks for the files — they settled it, and not in my favour: it was my mod.
Both saves are from the same tick, so they could be compared directly. In the whole 470 MB dump they differ in exactly one thing: your client had not drawn two overlay objects that the server had drawn, a recipe icon and its backdrop on an assembling machine. Everything else that differs follows from those two missing objects.
The cause: the mod steps aside when a player has ALT mode on, so it asked the game whether that player had it on. That value turns out to be a display setting, and each machine only keeps it up to date for its own player — for everybody else it holds whatever arrived with the map. Your client believed the other player on your server had ALT mode on, the server believed it was off. So the server drew the icons and you did not, and from there the two came apart.
Auto ALT mode had nothing to do with it, by the way: the version running was 0.21.9, and that setting did not exist before 0.21.12.
Fixed in 0.21.15. The mod now keeps track of ALT mode itself, from the toggle event, which does reach every machine — I set up a server and a client side by side to make sure of that before relying on it. One thing to expect when you first load an existing save with this version: ALT mode gets switched off once, for everyone. What each machine believed beforehand cannot be recovered, and off is the one value they are certain to agree on. A single keypress puts it back.
I have also asked the Factorio developers for the piece that would make the whole workaround unnecessary: A counterpart to only_in_alt_mode for LuaRendering
Thanks again for uploading the report. Without it I would still be guessing, and guessing in the wrong direction.