Try pulling the Ecobee Thermostat off the wall and then reattaching it to allow it to fully reboot. You might also want to reboot your HA system to see if that helps with the discovery process.
The pairing codes are either on the actual device, as part of the QR code for pairing HomeKit devices.... OR are shown on the screen as is the case with my Ecobee 3 Lite Thermostats.
What actual devices do you have in your house that are HomeKit capable? Unless you've been intentionally buying HomeKit capable devices, most users have very few of them in their homes. For me, my list of true HomeKit devices is relatively short. Maybe this list will help you identify the devices in your home?
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Lutron SmartBridge Pro - Paired with Apple Home directly
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Philips Hue Bridge - Paired with Apple Home directly
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LG Smart TVs - Paired with Apple Home directly
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Ecobee 3 Lite Thermostats - Paired with Home Assistant via HomeKit Device integration
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Aqara FP2 Occupancy Sensors - Paired with Home Assistant via HomeKit Device integration