Logitech makes a line of mice and keyboards (MX) that lets you pick from one of 3 bluetooth devices. MSFT has some too (their Surface line of accessories)
Pair this with a USB-C hub and it'll do exactly what you're looking for. If you get a PD capable hub it'll even charge your laptop via USB-C, eliminating 1 cable (on the desktop - still need one running to the hub)
USB-C hubs are a little pricey unfortunately. $50-450, depending on what you need.
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