How do I send non-ASCII keys over the BLE HID connection using an Adafruit nRF52 Feather?
Yo can use the keyboardReport() function to send key-codes with modifiers. Here is an example that will send an ! by sending the keycode for 1 plus a shift key modifier...

    // The keyboardReport() function takes an array of 6 keycodes. From what I can tell, it does not
    // press the keys consecutively,. it presses them simultainiously. 

    // Here we only want to send one code, so we back-fill the array with HID_KEY_NONE

    uint8_t keycodes[6] = { HID_KEY_1, HID_KEY_NONE , HID_KEY_NONE , HID_KEY_NONE , HID_KEY_NONE , HID_KEY_NONE };
    blehid.keyboardReport( KEYBOARD_MODIFIER_LEFTSHIFT , keycodes );  

    // This release seems to be required. Without it, the last pressed key just repeats forever. 
    blehid.keyRelease();   


The possible modifiers are listed here...
https://github.com/adafruit/Adafruit_nRF52_Arduino/blob/200b3aaefb3256ac26df82ebc9b5b58923d9c37c/cores/nRF5/Adafruit_TinyUSB_Core/tinyusb/src/class/hid/hid.h#L188

...and the possible keyscodes are listed here..
https://github.com/adafruit/Adafruit_nRF52_Arduino/blob/200b3aaefb3256ac26df82ebc9b5b58923d9c37c/cores/nRF5/Adafruit_TinyUSB_Core/tinyusb/src/class/hid/hid.h#L212

Unfortunately the hid_keycodes example does not compile, but bere is a ready-to-run example sketch showing how to send keycodes directly...

https://gist.github.com/bigjosh/5d8575f26988228dcf9d40c3795d0928