What does 'Cool On' or 'Heat On' flashing on my Honeywell thermostat mean?

This indicates the compressor protection feature is engaged. The thermostat prevents the compressor from restarting too soon after shutdown to avoid equipment damage. Wait 5 minutes for the safe restart time to elapse, then the message will stop flashing and the compressor will turn on automatically.

From the official Honeywell T6 Pro Smart Thermostat manual, page 5

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