Summary of what worked

Partion Table type: MBR
Partition Format: FAT32 or exFAT
Partition Size: 32768 MiB, rest unallocated free space
Drive used: 1TB SanDisk Professional 10Gbps USB SSD.

Issues I ran into

Only "removable" drives show up in the Windows Hyundai tool to write the update files to, "removable" is a bit set on the USB controller on the drive itself so is difficult if not impossible to alter. You can still copy the files manually onto your drive and it'll be detected by the vehicle.

GPT partion table drives will not be detected by the vehicle for updates. It took some trial and error to figure that one out. First I tested exFAT vs FAT32, then tried ensuring only 1 partition was on the drive with no luck, then tried changing GPT to MBR and that is what worked. You can see and change a drive's partion table type using partition manager on windows or similar tool on MacOS or Linux.

After thoughts

Since 32GiB FAT worked I do expect exFAT with a larger size would also work assuming you use MBR as the update size is very close to 32GiB and a lot of 32GB USB drives only have around 29 GiB of available space so can't fit the update files which would cause a lot of frustrated customers and dealers. I had that exact issue with my 32 GB USB flash drive which is why I went down the path of trying to get my larger and much faster 1TB USB SSD to be detected by the vehicle.

The vehicle told me 25 min eta for the update, I can't say how long it'll really take as I'm now going to sleep and don't feel like sitting in the vehicle for 30min to time it. Considering the file sizes I expect a USB 3.1 10Gbps drive will update much faster than a USB 2.0 480 Mbps or USB 3.0 5Gbps drive assuming the car can utilize the faster standard. I seen a 45 min eta on a YouTube video recently so I do suspect that the estimate is taking into account the USB bandwidth of the detected drive and cable.

I was using a 10Gbps USB male type-A to female type-C adapter, a USB 10 Gbps male type-C to male type-C cable, and a 10Gbps USB SSD. So assuming the vehicle supports 10Gbps USB on that port there should be no bottlenecks other than the write speed to its internal memory.