Syncthing

As someone else said, Syncthing. It's pretty much exactly what you're looking for. We use it internally at my company where we use all major OSes and devices.

What devices are we talking about? For phone to PC is use KDE Connect. It's reasonably fast 🤔

https://rsync.samba.org/

You could send files in your LAN via WebRTC

Trebleshot between phones and phones <-> PCs.

It is on F-Droid.

Between PCs in a same network, use Samba (some DEs allow to share folder in folder properties) or if you are in a dynamic environment (school) try KouChat which allow sharing files and not only LAN chat.

I think https://snapdrop.net/ might work for that?

What devices are you using?

I use KDE Connect and Dragit.

I use Warpinator for that

I use croc

The simplest to use is O&O File Direct, it very easy to use and encrypted end2end. But the problem is, it is not FOSS (Freeware) and only for Windows. Sad. I have put it just in case it is useful to someone despite this, because it is really good and safe.

Warpinator

Bluetooth does have very small bandwidth.

This version of the Bluetooth Core Specification was released before 2005. The main difference is the introduction of an Enhanced Data Rate (EDR) for faster data transfer. The bit rate of EDR is 3 Mbit/s, although the maximum data transfer rate (allowing for inter-packet time and acknowledgements) is 2.1 Mbit/s.

https://en.wikipedia.org/wiki/Bluetooth

Also newer bluetooth is faster, but sends the data via wlan

Version 3.0 + HS of the Bluetooth Core Specification[75] was adopted by the Bluetooth SIG on 21 April 2009. Bluetooth v3.0 + HS provides theoretical data transfer speeds of up to 24 Mbit/s, though not over the Bluetooth link itself. Instead, the Bluetooth link is used for negotiation and establishment, and the high data rate traffic is carried over a colocated 802.11 link.