Well, this is my first time hearing Betterbird
After reading their feature table https://www.betterbird.eu/#featuretable I think they have a really laudable goal.
I’d suggest to check the feature table first. If there is anything you concern, you pick Betterbird. Otherwise, you can choose one randomly :)
KDE Connect: https://kdeconnect.kde.org/
I also use Resilio Sync. It’s not open source software, but it’s self-hosted https://www.resilio.com/
There are also open source sync services, like nextcloud or syncthing