There have been lots of changes and accompanying improvements in bluetooth connectivity over the years related to the bluetooth standards, the bluetooth transceivers, and the bluetooth software in the computer. But the process is pretty much automatic and there is very little or no "configuration" available at the user level. The best improvements I have encountered were the result of hardware and software (macOS) upgrades. So I don't think it is a configuration issue.
That does not mean there is nothing you can do to improve connectivity...
- Be sure to Turn your mouse and keyboard on BEFORE you boot your computer so they can be seen at the most opportune moment in the boot process. (I never turn either of mine off because the power drain at idle and effect on battery life is negligible.)
- Weak batteries can mean weak signals, so be sure the keyboard and mouse batteries are kept well charged.
- Be sure there is minimal, preferably no, physical barrier, particularly metallic, between your computer and your Keyboard/mouse.
- Be sure you are running the latest possible version of macOS (in my experience, it can make a significant difference)
- It sounds as if you may have an older model keyboard, consider upgrading to a newer model with a newer model bluetooth transceiver
- If all else fails, connect the keyboard to directly to the Mac with a USB cable which terminates the bluetooth connection and turns your keyboard into a wired device while it is charging. (I had to do that during the early macOS 12 betas to assure good connectivity but that was fixed by beta 4)
