When one agent represents both the seller and the buyer in the same deal, that is called dual agency (or in some states, transaction brokerage, where the agent acts as a neutral facilitator rather than an advocate for either side). What happens to the commission in that situation depends entirely on what your listing agreement says.
Most listing agreements specify a total commission percentage and a cooperating broker split separately. If your agent finds the buyer themselves, the cooperating broker split does not automatically disappear. The listing agreement you signed likely still entitles the brokerage to the full combined amount unless the contract explicitly states a reduced rate for in-house sales. Some brokerages do write a lower rate into the agreement for that scenario. Most do not.
So in a concrete example: say the agreement is 5% total, structured as 2.5% listing side and 2.5% buy side. If your agent brings the buyer, the brokerage commonly keeps all 5%. You would need a specific clause reducing that to 2.5% (or some other number) for the savings to reach you.
The place to look is the section of your listing agreement that covers in-house or dual-agency transactions. If you cannot find that language, ask your agent directly before you are in that situation, because negotiating it after an offer arrives is much harder.
One thing worth knowing for the Akron duplex when you eventually list it: this is worth raising at the very beginning of the listing conversation, before you sign anything. You can ask for a reduced commission if the listing brokerage brings its own buyer, and some agents will agree to it. You have more room to negotiate that term on the front end.
What does your Cleveland listing agreement actually say about in-house sales? That will tell us whether you have any protection already written in.