KDE Connect should fit the bill; despite the name, you don't need to be using KDE (or Linux even) since there are clients for every major OS, even mobile.

Among many other cool features, it lets you easily and simply just send a file from one device directly to another on your local network. I use it all the time to send photos from my phone to my desktop without plugging anything in, for example.

Much simpler and more direct than the other suggestions: LocalSend.

Also fully open source, local only, cross platform. Only works in the same network, obviously. That's the point.

I think ShareDrop does that.

Others told about snapdrop, sharedrop, localsend etc.

But depending on what devices you are talking about, you might do with just an http server.

I have a file manager on my (android) phone with a http server built in, and my laptop is connected to it via WiFi hotspot all the time. I just start a server on my phone and use a browser or any other download tool (curl, wget) to transfer files from my phone to my laptop.

If you have python installed, you can run an http server on any device you have (for example, a laptop) via python -m http.server and access your files from any other device on the same network by manually typing your local IP into a browser.

RSync, scp, rcp, SMB, sneakernet, plus numerous third-party tools. It depends on the platform and exact scenario.

There’s an app called Local Send that’s like an alternative to air dropping files on iOS devices, not sure if that’s what you’re talking about or not.

Syncthing accomplishes both local and Internet transfers and doesn't need a third party server (if you're not doing NAT traversal). I don't think you can send individual files through it's interface. But you can share a directory and any files you add (or edit) will sync via P2P to other devices.

LANDrop has an app for every operating system and android/ios

I run a local instance of www.snapdrop.net in docker off my Synology NAS. Works great!

Warpinator

If you are inclined to do things that way there's also the python Fileserver $ python3 -m http.server 8080

Android devices have this function natively built in

Wormhole (a command line tool) is also a good choice. It works in lan but also over the internet.

You can't really do this on the web as devices can't directly connect to one another. You need some signalling server to bootstrap the transfer. However almost all of these WebRTC services will actually do the transfer locally if both devices are connected to the same network and can talk to one another directly.

So you would need a native application.