Bluetooth Magic mouse & keyboard don't work in boot picker, but do at login screen

I installed Ventura 13.7.7 with OCLP on my 21.5" iMac mid 2010 (iMac 11,2), but the original Bluetooth Magic Mouse & Keyboard don't work at the boot picker; however, they do work with the login screen for Ventura.

Furthermore, the magic mouse randomly disconnects and sometimes reconnects while in the OS. There were ZERO issues with the mouse and keyboard before I erased my boot drive (500GB SSD) through Disk Utility that had stock macOS High Sierra.

I should note that I tried many times to install Sequoia and Ventura without erasing the SDD via Disk Utility and simply doing an update, but it wouldn't work. Then I did a full erase in Disk Utility which allowed me to install Sequoia. Sequoia was super slow, so I wiped again with DU and installed Ventura. Ventura works as fast as expected.

After doing the Disk Utility erase, I had to use a USB mouse and keyboard because I couldn't get the boot picker to activate with holding OPTION down.

I would most certainly appreciate any help in these two Bluetooth matters.

21.5" iMac 11,2 mid 2010 3.06GHz Dual Core Intel i3, ATI Radeon HD 4870 256 MB, 16GB 1333MHz DDR3 RAM, Ventura 13.7.7. Installed using OpenCoreLegacyPatcher 2.40. 500GB SSD. Original Apple Bluetooth Magic mouse and keyboard (without the numeric keypad). Brand new batteries (Tried many), cleaned contacts with alcohol).