Well, I'll answer my own question since it might help others. The problem is the error message in the Authorize.net response is really vague.
Kurt Friars' comment was helpful, since it pointed me in the right direction. As for Mansour Hamcherif's suggestion, the merchantAuthentication object was set in my app, it just didn't have the right values, so it wasn't that.
The solution for me was setting the proper values to setName() and setTransactionKey(). The previous developer who had worked on this project had left values and the credentials had expired. I did a Linux text search for "setTransactionKey", which lead me to the correct PHP file where I need to set:
$merchantAuthentication = new AnetAPI\MerchantAuthenticationType();
$merchantAuthentication->setName('EnterYourLoginNameHere');
$merchantAuthentication->setTransactionKey('EnterYourTransactionKey');
After that, I cleared all of my Laravel app's caches as well as my browser's caches, did a hard reload, tried a transaction again and it worked! I got:
This transaction has been approved., Transaction ID: **********.