Well first, if that was the real value, as @ignoramous says, rotate it. Which would mean at the very least it needs updating in Fly or Google.
You can check whether Fly has done its bit by connecting to your app instance by running fly ssh console from the folder your fly.toml file is in. That should load you into the vm, and then run e.g echo $SEARCH_CONSOLE_PRIVATE_KEY. If that shows you your private key, well Fly’s bit is done at that point. You provided an environment variable, and in turn Fly passed it to the vm when it booted. Beyond that point, it’s down to what you do with it in your code/SDK.
On the other hand if the value is not shown, well yes, that would be an issue with how the secret is being passed in. In which case check out what @ignoramous suggests about loading it from a file instead.