HomeKit does not support "exporting" devices, whether via HomeBridge or any other means, to third-party systems -- only the integration of other devices into HomeKit. To get anything out, you'll have to use a workaround, like importing a device from that third party system into Home and then using a Home Automation to communicate between the two. This is easy for things like switches, even if a bit tedious to set up; it will get trickier and possibly impossible for 100% functionality for other devices like thermostats.
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