Have you tried syncthing-fork? You can synchronize folders across the internet with it between all sorts of devices, including android. No middlemen required since it's peer to peer.
Its file sharing feature works between any supported devices, including phone-to-phone, and yes, it is intended for connections across a local network.
If the file doesn't exceed 2 GB, you can use this : https://lufi.ethibox.fr/
Files are encrypted and cannot be seen by the owner of the website and the share can only go up to 30 days. It is recommended by Framasoft, the ones behind peertube.
Interesting alternative, thanks. SimpleX is the only one, as far as I know, allowing chronology since it has a chat and all, you can probably use also matrix protocol the same way but it require an account.
Syncthing does work across the internet. It uses nat hole punching to achieve this. Unless your network is behind cgnat / double nat I believe. Me and my buddies use it all the time.