I have two boards: Raspberry Pi Pico 2W (RP2350) and Raspberry Pi Pico W (RP2040). Connecting a BLE keyboard to them works in v4.4.4 and below but stops working in v4.5.0 and above (up to the latest v5.4.1).
Note that BluetoothHIDMaster::connectBLE() properly returns true in any of the versions I tried as soon as I put the keyboard into pairing mode. However, in versions 4.5.0 and above, BluetoothHIDMaster::connected() never returns true after that and onKey* and onMouse* callbacks are never called. In v4.4.4 and below, everything works as expected.
Reproducibility is 100% here, it doesn't make any difference which of the boards I try and which of the keyboards I try to connect to them (I have two completely different BLE keyboards).