Thanks for the feedback. Syncing conversations between multiple devices is a bit tricky due to the fact that synced conversations are saved locally. That being said, the sync button at the bottom right is designed in a way that if you click on it it does two things:

1- It looks at your list of conversations and compares the id of each chat with the list of conversation ids from ChatGPT. If there is a missing chat id in your local version, it will automatically downloads it from ChatGPT and sync your local chats.

2- Whatever chat you are looking at when you click on the sync button, will automatically get overwritten by what is saved on ChatGPT. That means that if you make changes on your phone and then want to continue the same conversation on your desktop, all you need to do, is to go to that chat, then click on the sync button to download the latest version of that chat.

You are probably thinking why do I not sync all chats "AND THE MESSAGES INSIDE EACH CHAT" without needing you to click on the sync button. The answer is, to do a deep sync of all chats, it requires me to download every single chat and compare it with what you have locally, and do that within the first few seconds of you logging in to ChatGPT. With the current rate-limiting that ChatGPT applies, this is technically not possible. If I try to download every chat to compare them you will get rate limited very quickly. So the easiest way is to just let the user decide which chat needs to be updated due to changes on other device. All you need to do, is to click on the sync button while you are on that specific chat, and that should guarantee that you have the latest version of that chat.

Hope that helps.