Hello @sm1thy
Your system uses a Sunflower motherboard which uses a proprietary power supply because of its small size and proprietary connectors. Your 180W PSU isn't powerful enough to support anything significant as far as graphics cards go.
HP does have up to a 310W (L03980-800), 400W (L04618-800) and a 500W PSU (L05757-800) that can connect to the Sunflower Mobo. The 500W might not quite fit the screw holes all the way. Link to user that tried it.
If you can get one of those PSU's, you can connect a mid level graphics card fine, as long as it fits the available space in your desktop. You would need to measure the available space with a tape measure, then compare it to what ever cards specs you can find to fit. You could run a GTX 1060 or RTX 2060 mini card easily with the 500w PSU. Or a GTX 1050ti with the 310 or 400W version.
HP Parts Surfer is what you would use to order it... http://partsurfer.hp.com/Search.aspx?searchText=L05757-800
But it looks like your desktop was sold in either Australia or New Zealand and the parts surfer doesn't show that PSU as available their. Not for the 310, 400 or 500W PSU.
Perhaps you could Google it and come up with something.