Manually setting show/episode to finished in jellyfin doesn't update watch status on providers. about jellyfin-ani-sync

[vosmiic]

Hi, there is an option in the plugin settings under the "test save location" button to update the provider after ticking shows as completed.

This should fulfil the functionality you are looking for. As the little note says, the feature is new and I personally don't use the feature so it has not been heavily tested.
Also, as a potential fix to your alternative problem, I have been using the Jellyfin Kodi plugin and it works wonders on my Shield. I found the official Jellyfin app to not work very well (its still being developed so its understandable). Also the Jellyfin Kodi plugin sends the progress update back to Jellyfin, so I don't have to manually tick anything as completed to get the plugin to send the update to the API.
Please do open the issue again if this has not fixed the incident, or if you have any other questions about the plugin.