He Nschurmann!
Based on your post, you'd like the ability to use the Dvorak keyboard at the login screen and have issues with your Logitech MX Master 3 Mouse. We have the answers for you.
To have the ability to change the keyboard to Dvorak at the login screen go to System Preferences > Users & Groups, select on your user, then Login Options on the left under the sidebar. It will provide some options, but you'll want to unlock that padlock with your administrator password on the very bottom left to make changes here. Once unlocked select on "Show input menu in login window" to have the ability to see the keyboard input in the menu bar when logging in and lock that padlock to save the changes.
Sometimes to reconnect the Bluetooth mouse, you can tap on the buttons on the mouse to wake it up and the Mac should then pair them once again. If that doesn't work, then you can Reset NVRAM or PRAM on your Mac This resets a small amount of memory that your Mac uses to store specific settings and access them pretty quickly, which might resolve this.
If not, try to forget or remove the mouse and re-pair it with your Mac: Using a Bluetooth mouse, keyboard, or trackpad with your Mac under section, "Remove a Bluetooth device from your Mac" and then the section on, "Pair your Mac with a Bluetooth device".
Should that not resolve the issues with your Bluetooth mouse, do you have this issue when the mouse is paired to another device? Have you noticed any other Bluetooth concerns with your Mac? For example, when using Bluetooth headphones?
Wishing you the best!
