[Bug] Mouse keys prevent keyboard from starting up when switching inputs using KVM switches

Describe the Bug

I had submitted #15939 but, after finding other users reporting issues with KVMs when enabling mouse keys, I see this is a common issue. Even though KVMs used to be a niche thing, people are using them more with WFH and all that, so maybe it's worth taking a look into why that happens.

My understanding is that QMK will present two devices (a keyboard and a mouse) connected through a hub and that is the cause of those issues.

System Information

• Keyboard: GMMK Pro, JJ50, Planck EZ
  • Revision (if applicable):
• Operating system: Windows, Linux, macOS
• AVR GCC version: various

• ARM GCC version: various

• QMK Firmware version: various

• Any keyboard related software installed?
  • AutoHotKey
  • Karabiner
  • Other:

Additional Context

I haven't been able to identify why that could be happening at all. Would appreciate input on where to look, if any bits are suspicious.