It's the tiny motherboard that is the issue. The main board power connector is too close to the PCI-E slot. There is no way to fit 90% of graphics cards in there. It has to be a super short one less than 6 inches. Maybe if there is a single slot card? But most cards are double slot nowadays.
I could get a new motherboard in addition to a case but I am exhausted with this project at this point and I will be happy to get a 1050 ti in there for a backup editing computer.
I am much happier with the clearanced out ice cube LEDs I bought.
You can filter results on PCPartpicker, for length of graphics card. It's hard to say how much room you're gonna have for sure, since I'm only going off the mobo specs on HP's website, and scaling it to get a general idea of how much room you have (up until the CPU connector), but from what I can tell the absolute longest graphics card you can get is 158mm +/- 1mm. The absolute smallest GTX 1050 Ti I can find is 145mm. Here's a list of the GTX 1050's and GTX 1050 Ti's that are under 150mm (most single fan graphics cards seem to have either a length of 145mm or 155mm, and I think the latter is cutting it a bit too close).
If you want something bigger than that, you're probably gonna have to get a new mobo and case if you're adamant about using a graphics card.
Here's the two cheapest mobo's and cases I could find on PCPartpicker: