Owner of a first generation Logitech MX Master [1] and MX Keys S here, frequently switching between two Macs. Every time the mouse has to be turned over to access the button at the bottom, and keyboard has to be switched on it's own.
Logitech finally released an Options+ feature [2, 3] to switch multiple peripherals at the same time, with a single key press. The only problem - my ol' reliable isn't supported. It's a Unifying device, and only Bolt is officially supported. [4]
So, I made a fix - The Mouse Is Coming Too. There are 3 mini-apps, each coresponding to a different host device. Running any of them will switch both the mouse and the keyboard to a given host. They are mappable to "Open application" in Options+, so a programmable key can be used to trigger them.
Tested with MX Master and MX Keys S, but should work with any models recognised by Options+
[1] v1, bough some 9 years ago, and released in 2025. Still going strong after some ~9 years, micro-USB to USB-C conversion, skates replacement, stuck thumb button [5], and more than a few falls
[2] Yes, I should switch to something better
[3] https://marketplace.logi.com/releasenotes/optionsplus/en#2.6...
[4] To make it a bit more absurd, "easy switch" for this mouse already exists and works, but is accessible only through Options+ Action ring. Tried giving it a fair chance, but it's too cumbersome.