It appears the size of the card determines if it can use more than 30 watts on a PCIe slot
All sizes of ×4 and ×8 PCI Express cards are allowed a maximum power consumption of 25 W.
All ×1 cards are initially 10 W; full-height cards may configure themselves as 'high-power' to reach 25 W, while half-height ×1 cards are fixed at 10 W.
All sizes of ×16 cards are initially 25 W; like ×1 cards, half-height cards are limited to this number while full-height cards may increase their power after configuration. They can use up to 75 W (3.3 V×3 A + 12 V×5.5 A), though the specification demands that the higher-power configuration be used for graphics cards only
I was cleaning my PC out today when I noticed that it said 35W next to my PCIe port. I have no idea if my PC has a watt limit on my PCI or what, it's Dell Optiplex 960 SFF, it comes with 235W PSU stock so I though maybe Dell wrote that incase someone wants to put a GPU in with stock PSU and it...
if your case only allows half height cards they may be restricted to 35
I have seen it suggested to try a card that wants more, but if that fails use a 1030 or similar card that uses less than 30 watts
Limitations on the gpu too. Most modern gpus after the 900 series? don't use much (if any) other voltage than 12v, so may not be able to claim the full 75w, only able to physically use @ 65w. Which might not be enough for something like a 1050 with a 70w - 75w possible draw.
You'd have to research individual cards to make sure they have a lower pcie slot draw, relying mainly on external 6pin power instead. If that's possible with your psu.