What you have is a wood burning zero clearance fireplace with a gas fire starter. This allows you to use gas to "start" a wood fire and then turn the gas off.
The good news for you is if you want to convert to gas logs, the gas line is already to your fireplace which makes that conversion super easy.
You can find a very nice set of has logs for $300 to $500, however, they aren't efficient due to most of the heat going straight up your chimney.

If you want to burn gas, but also want energy efficiency and warmth, you should look at a gas insert for your fireplace. An insert has a sealed glass front so you don't lose room air up your chimney and you get a lot of heat circulated back into your room. An insert includes a chimney liner kit that will be installed inside your existing fireplace chimney. Cost of an insert would be $2500 to $4500 depending on how much quality you wish to invest in.
Gas logs are cheaper, but inefficient. Gas insert costs more but can reduce your heating bills by letting you zone heat your family room where you spend most of your time.
Either way, have a local hearth professional inspect your existing fireplace and chimney to be sure it's safe to convert.

We had a similar fireplace in a previous house. The gas starter made starting a wood fire amazingly easy, so we actually used it quite a bit. When the wood has started burning ,you just shut the gas off. My suggestion would be to live with for a while this winter and see if you like it just the way it is...just a thought.

Thank you both for your advice! the $2500-$4500 is probably above my budget right now, with the other work I need to do first. But I like the idea of a super-efficient fireplace.

I'll probably do what rocketjcat suggests and try it out as is first. The seller has agreed to do the safety check before closing, so I hope to piggyback on the call to learn more about the setup I have.

u sure can it will covert over

HU, I’ve gotten nothing but the runaround from local fireplace vendors on this idea. No luck so far in finding someone I’m sure knows what they are doing.