I can tell you right now that this isn’t going to work. If you open the same profile on different devices at the same time, you’re basically bound to end up with conflicts. The only way for such a synchronisation to work would be to completely close Thunderbird on the first machine and let everything sync first, and only then open it on the second device, and vice versa.
You could theoretically sync only your local e-mail account folder (when using POP3), but Thunderbird doesn’t support that either. Mainly, it’s incapable of detecting changes that happen on the disk while the program is still open. It needs to be closed and re-opened in order to do so (or you could use the “repair folder” button, which is still too cumbersome to be practical).
You can also check my older thread about the very same problem at https://forum.syncthing.net/t/using-syncthing-to-synchronise-e-mail-locally/16079.