Don’t register the remote to the Broadlink cloud. Just do the initial setup through the Broadlink app on your phone to connect the remote to your WiFi. When you see the remote is within your LAN stop using the official Broadlink app on your phone and continue the setup through HA.
Also learning IR/RF commands through HA is somehow not very reliable and often produces incorrect codes. I use Broadlink Manager for learning commands. More about the latter here.