For the F-droid enabled users, it seems there’s a Syncthing app in the Termux repos:
~ $ apt show syncthing
Package: syncthing
Version: 1.28.0
Maintainer: @termux
Installed-Size: 26.4 MB
Homepage: https://syncthing.net/
Download-Size: 7857 kB
APT-Sources: https://packages.termux.dev/apt/termux-main stable/main aarch64 Packages
Description: Decentralized file synchronization
Termux (on F-droid) is a userland environment that runs on top of your Android device’s kernel. It has Debian/Ubuntu-like package management system that pulls from repos maintained by the termux team. If the package is available for aarch64, its probably available in the termux repos. Its not so much of an app as it is an alternate userland that runs on top of the same kernel, but can interact with Android a couple of different ways.
The main Termux app gets you a basic command line environment with the usual tools included in a headless Linux install. From there you can select your preferred repos, do package updates, installs, etc, just like on a desktop or laptop. You could even install a desktop environment and use RDP to access it.
Then there are some companion apps that are useful:
So you could install the syncthing package in Termux and (after setting up Termux access for your internal storage) configure it to sync folders from your phone to wherever syncthing syncs. You’d set up a start script under Termux:boot to launch it when your phone starts, or Tasker to start/stop the service on your home WiFi.