I think F-Droid will have to go the ADB route, maybe have a desktop interface to wirelessly ADB install APKs to your devices... could be an awesome way to manage apps on multiple devices! I currently have a powershell script to do all that myself.
You can already bootstrap an ADB connection to your own device without any extra hardware via Shizuku.
Won't be long until F-droid releases a plugin that does the installation via Shizuku.
Permik|4 months ago