And where would the key be stored ? If it's on the same server and if Flarum can read it, what is the probability the bad guys get access to it as well ?
I think Laravel encryption was made for encrypting values that will be stored outside of the app's control, like cookies or export files.
Here's some interesting reading:
https://security.stackexchange.com/questions/16939/is-it-generally-a-bad-idea-to-encrypt-database-fields
https://security.stackexchange.com/questions/4755/web-application-encryption-key-management
EDIT:
Also I think API keys are the least of your concern. They can be easily revoked or rotated with minimal effort or impact. Exposed private user data is probably way more problematic.
This will of course depend on which thiry-party services you have API key for in your forum. Right now the extensions we have dealing with API keys are mostly for oauth or readonly data I believe, so probably a limited impact until you're aware of the breach and revoke access.