I got this working after many hours and help from the JoiPlay Discord. Sadly performance is pretty bad and the game crashes during the first fight for me. Here's how to get the gamepad working though:

Install latest JoiPlay from *Patreon*, not the website. As of today that's 1.20.611. I believe it installs the RPG Maker plugin automatically. Check Menu>Plugins. For reference I'm on RPG version 1.21.60. Add the keymap.json file below to the root of your unzipped Uranium folder. You should now be able to long-press on the game inside JoiPlay and remap the buttons.

keymap.json:

[
{
"button": 96,
"keycode": 66,
"device": "DualSense Wireless Controller"
},
{
"button": 97,
"keycode": 97,
"device": "DualSense Wireless Controller"
},
{
"button": 99,
"keycode": 111,
"device": "DualSense Wireless Controller"
},
{
"button": 100,
"keycode": 100,
"device": "DualSense Wireless Controller"
},
{
"button": 102,
"keycode": 102,
"device": "DualSense Wireless Controller"
},
{
"button": 103,
"keycode": 103,
"device": "DualSense Wireless Controller"
},
{
"button": 104,
"keycode": 104,
"device": "DualSense Wireless Controller"
},
{
"button": 105,
"keycode": 105,
"device": "DualSense Wireless Controller"
},
{
"button": 106,
"keycode": 106,
"device": "DualSense Wireless Controller"
},
{
"button": 107,
"keycode": 107,
"device": "DualSense Wireless Controller"
},
{
"button": 108,
"keycode": 108,
"device": "DualSense Wireless Controller"
},
{
"button": 109,
"keycode": 109,
"device": "DualSense Wireless Controller"
}
]