My laptop has a single audio jack and when I plug in my earbuds, they work fine, but if I plug in the green audio cable of my Logitech G230 headset into the same jack, it will not play audio. The device shows up specifically in sound devices and when tested, it will show audio as being played but the headset doesn't actually play anything. I've been using the same headset with both mic and audio jacks in a USB adapter from Logitech and plugged into the USB 3.0 port and it works fine there. Is this a driver or hardware problem?
Sounds like it is the 3.5mm jack on the laptop. If that headset has a mic (which I am assuming it does) then that could be the problem there. Not that there is anything wrong with the headset, but some jacks on laptops that are output only can have problems if you connect a headset. No matter if it has a single 3.5mm or two (one for input and one for output) on the headset.
The only solutions I have found is either to replace the jack on the laptop (which doesn't always work to resolve it and can be costly). Or to get a 3.5mm to USB adapter, which you did. That almost always is the best fix.
The laptop jack is probably for a four-conductor plug, and the speakers only have three. You'll need an adapter to break out the speaker and mic connectors separately; they exist, I've bought some, I think on Amazon.