Why does Windows think that my wireless keyboard is a toaster?

Reason 1

Because Microsoft made a toaster driver sample. In the sample there is the line <DeviceIconFile>Toaster.ico</DeviceIconFile> and there is a chance that your keyboard manufacturer took that sample.

Reason 2

Look at the back of the keyboard for some place to insert a slice of bread…

As for "why specifically a toaster", "Toaster" is an old catch-all name for "any arbitrary device." For example, you can find "SCSI toaster" alongside "SCSI disk", "SCSI tape", and even "SCSI scanner" (yes, scanners used to be on SCSI) in some very old Microsoft slides depicting the storage stack.

Windows recognizes device type by what the device says it is which in the majority of cases can be overwritten...

If you have plugged in an actual thumb drive (confirmed by observation) it could be because there is malware/virus on that device.

This is a technique used by impostor software to for example show up as a keyboard so windows will trust it automatically yet act as a key-logger...

Never had experience with a 'smart' toaster so it depends, did windows trust it (install and allow its usage) without any consent?

Note: this scenario is unlikely, but note it ;)