I don’t know of an off-the-shelf way to implement what you want. There’s a usb-usb converter in QMK which allows you to add QMK features to any keyboard, but QMK does not have Bluetooth support. ZMK is designed for Bluetooth but doesn’t seem to have anything like QMK’s protocol converters (tho I might have looked in the wrong place).

You might be able to DIY it with a Raspberry Pi Pico W, by gluing together the picow_bt_example_hid_host_demo and tinyusb_dev_hid_multiple_interface examples from https://github.com/raspberrypi/pico-examples

In principle, yes, but you'd need something additional to act as a Bluetooth host. You'd probably be better off using a part that can do both, like an ESP32.