Hello, the wonderful Raspberry community,
I wanted to share my recent open-source project with you, possibly some of you will find it useful.
I have built a Bluetooth HID hub, which can run on Raspberry Pi (Zero W is enough, certainly works on 3B+/4B). You can connect your wired or wireless keyboard and mouse to RPi running the BT HID Hub. The Hub will present itself as a Bluetooth keyboard+mouse device to your computer(s) and channel the input from your devices to your computer(s).
This is pretty unusual, as Bluez, the Linux Bluetooth stack, does not support simultaneous host/device mode, so I had to modify Bluez.
You can also remap the keyboard keys or other HID events (currently I remap my Apple wireless keyboard keys). I built it in Python, so should be pretty easy to implement any custom HID event mappings for any of your devices.
Furthermore, the hub can be simultaneously connected to a number of computers and you can easily switch between the current computer with a key combination. So you may have a single keyboard/mouse to work with a number of machines, no matter what OS you run on those.
Super useful if one of your machines is a laptop, which you carry around - in this case, you don't need to replug your input device when you come back to where they are.
RPi just needs to be around and powered, no need to plug it to the host machines. Controllable (pairing etc) via a web interface. Includes an automated installation script for a fresh copy of Raspbian.
Here it is: https://github.com/ruundii/bthidhub
Enjoy.