Satechi X3 keyboard and M1 Mouse will not connect (via bluetooth) until after login

I own a 2017 T1 15" MacBook Pro running OS Ventura 13.6.7.

I recently purchased a Satechi X3 keyboard and M1 Mouse. I have discovered they are not recognised until after logging into the computer. I do not experience that problem with an Insignia bluetooth mouse.

I contacted Satechi support and have not resolved the issue. Their last advice was to contact apple.

As part of my troubleshooting I have:

Confirmed that the mouse and keyboard will connect at login with my M2 Mac mini and M2 MacBook Air

Followed all steps to disconnect and then pair both devices with my MacBook, clear bluetooth plist, reset bluetooth via terminal command, reset SMC, and reset PRAM. As a last resort, I turned FileVault off and the problem went away. I have since enabled FileVault and problem has returned.

I am unsure as to why other 3rd party bluetooth devices I own will connect at the login screen, however, the Satechi Devices will not connect until after I have logged in using the built in keyboard and trackpad on my MacBook Pro.

[Re-Titled by Moderator]