For connecting FWL16 keyboards, you can find a compatible connector here: External USB-C enclosure for input modules - #2 by C_Scott_Ananian. Some options for a USB-to-Bluetooth adapter, including DIY ones: github.com/joric/nrfmicro/wiki/Alternatives#usb-to-bt-adapters, €50 with built-in battery sterling-key.com, $30 handheldsci.com/kb.
If you’re ok with a more involved project, and want the best battery life, then ZMK is the way to go imo. zmk.dev/docs/hardware. For a FWL16 keyboard, you’d replace the onboard microcontroller with a ZMK supported one. For a FWL13 keyboard, those don’t have onboard microcontroller. The FWL13 keymatrix pinout should be on FW’s github. How its columns and rows map to keys can be found here: howett.net/data/framework_matrix.