I did some more digging, and apparently this is a common issue with the C3 chip in general. There is a protocol difference between the standard ESPs and the C3s, and that has to be defined in the librarys BleKeyboard.cpp file. Thanks to @maker114 on github for answering the issues awhile ago, and thanks to google for letting me find it lol. Heres the entire thread for future readers.
More specifically, I edited line 130 in the BleKeyboard.cpp file of the library as follows:
//pSecurity->setAuthenticationMode(ESP_LE_AUTH_REQ_SC_MITM_BOND);//default security protocol. Changed for C3 as per github issue reccomendation
pSecurity->setAuthenticationMode(ESP_LE_AUTH_BOND);//for ESP32-C3 Protocol
Also, after changing this, I was able to use the current BSP (3.0.2) without issue. This protocol difference also explains the weird authentication errors I was getting in the serial monitor. Thanks again for the help