I have a Mac Mini from 2018, Sequoia 15.4.1, an older Apple magic mouse and USB APple keyboard (small version). All of Sequoia, this mouse fails to scan and connect at power-up and the login screen. Which means there is no way to move the cursor at the login screen, which, when there are two login users, I cannot click my "User" icon to log in. Dead at the login screen!
So I have to keep an old USB-A mouse with cable, plug it in, navigate the cursor to the login prompts/icons, and after the system boots the OS it connects to the mouse. Weird, because the apple bluetooth keyboard almost always connects with no problem. Over time with Sequoia, it started gradually: sometime mouse found, sometimes not. Sometimes it wouldn't scan and recognize the keyboard, but that seems to have not happened recently and was resolved by a power cycle of the keyboard.
And YES I have tried switching these devices on and off, many times, to see if it would "seek and find" with a mouse power cycle, and YES they are fully charged. This is stupid, Apple broke Bluetooth, or BIOS chooses to not scan for older devices? These devices are 9 inches from the MacMini.