How do Logitech keyboards coexist? What if I mix up the USB dongles?

There are at least two types of Logitech dongles (the modern ones, without "pairing" button). The newer ones are so-called "unified receivers" and marked with orange flower-like logo. The "unified receivers" can be modified with Logitech software and can be paired with any qualified device.

Older dongles (of exactly same shape) were paired only to the particular device, so they must be kept together, and usually the devices have an internal compartment to hold the dongle. Yes, it is inconvenient.

Each Logitech RF device has an unique identifier out of 65,000 available, and proprietary Logitech RF communication uses 78 channels (in 2.4GHz band). This white paper from Logitech indicates that interference-free communication can work up to 78 devices in 10m proximity.

The USB dongles are usually "Logitech unifying receivers" and, while initially paired with a particular device, are not permanently tied to it. You can pair a device with the dongle using Logitech's software.

According to Logitech's support article about it, a single unifying receiver can pair with up to 6 Logitech devices.