As it bothered me that rescript-vscode requires a manual save to update error reporting, I found out a little workaround.
Just use autosave by adding this to your settings.json:
  "files.autoSave": "afterDelay",
  "files.autoSaveDelay": 200,
It seems that autosave does not include formatting, so you do not need to disable formatOnSave.
NOTE: I only tested it in smaller files. If it affects performance too much, you could tweak the delay a bit.