According to this Ohio lawyer, you are right, or at least you were right as of 2013.
https://www.thelawofficeofbrianjones.com/blog/2013/02/intruders-and-the-castle-doctrine-in-ohio/
According to info at the link, to be covered under Ohio's Castle Doctrine, a dwelling must be designed to be occupied at night. That does not describe most garages, attached or unattached.
Following the link in post 226, I saw this:
***“The recent change in that law deals with the burden of proof,” he said. “The burden of proof is now on the state, which includes our detectives and prosecutors to prove that the case was not a case of self-defense, whereas in the past, the burden of proof was on the homeowner or person claiming self-defense.”***
It also appears that the Castle Doctrine is ambiguous in Ohio as to whether or not an unattached garage is covered by that law.