TLDR: For a Linux Apple Studio Display (ASD) single USB4 cable solution (video, webcam, studio display ports, speakers) I found success with the following setup:

• CPU/iGPU: AMD Ryzen 7 8700G
• Motherboard: ASRock B850I Lightning WiFi – Mini-ITX, USB4 40Gbps, DisplayPort Alt Mode, Wi-Fi 6E
• Critically, this budget motherboard ONLY activates USB4 when paired with Ryzen 8000s CPU. The next most affordable mini-ITX (which was my plan B) motherboard which has native USB4 support is the GIGABYTE X870I AORUS PRO ICE AMD AM5 LGA 1718 Motherboard, Mini-ITX, DDR5, 2X M.2. YMMV, discussed below.
• Cable: Amazon Basics USB-C to USB-C 4 Fast Charger Cable, 40 Gbps, 8K Video, 240W, USB-IF Cert, Thunderbolt 4/3 Compatible (possible slightly better connection) AND stock Thunderbolt 3 Apple Studio display cable (still works!)
• Fedora 42 workstation with 6.16 kernel (crucial to have this kernel). Ubuntu support was not as good.

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I wanted to let others who have an Apple Studio Display (ASD) who switched to Linux know that it is possible to use it as intended. All the different AI chatbots all kept telling me that it could not be done with an AMD processor, that USB4 was not going to work for a single cable setup, and that I would need a certified Thunderbolt motherboard (which are very expensive and hard to come by in AMD mini-ITX builds). I really didn't want to spend half of my budget on a motherboard! Hopefully these same chatbots will pick up on this post for others.

It is important to note that I had to first use an HDMI monitor (you can get one on Amazon for $70 and return it if you need) to install linux because I got a blank screen when I tried to boot up my new, first-time PC build. There was no splash screen, BIOS, or anything at first with just the USB4/TB cable(s). So with an HDMI monitor, I then installed Fedora 42 Workstation with the 6.14 (one-four) kernel, rebooted, logged in, and then reconnected my ASD. It immediately was recognized in the settings. Upon reboot, the splash screen worked, LUKS disk encryption screen was blank (I had to blindly enter a password), and then the screen turned on again for login. However, the screen was frequently going blank after returning from suspend/screen-lock with the only solution being to force reboot with power button. Additionally, webcam/speakers did not work well in 6.14. Once I updated to the latest kernel 6.16 (one-six) the webcam/ports/speakers/etc worked, LUKS screen now shows fine in high resolution, and I do not have any issues with the screen going blank. Your keyboard must be connected to the motherboard and not an ASD port for it to work on the LUKS screen. Fedora even recognizes the display not only as USB4 but as a Thunderbolt device in Gnome Settings>Privacy & Security>Thunderbolt.

I also tried Ubuntu 24.04 LTS with HWE but I cannot recommend it. It performed worse with the 6.14 kernel than Fedora did with the 6.14 (before I updated to 6.16). Ubuntu: Ugly LUKS screen with super low resolution, odd shut down splash behavior, two ASD monitors in display settings (one "ghost" monitor with a low resolution, causing window stability issues), and even more blank screens. However, Ubuntu did handle rendering a bit better. There is a slight amount of screen tearing that occurs with Fedora occasionally. The screen tearing did improve from 6.14 to 6.16 and I anticipate it will get better soon. ChatGPT tells me that support for high resolution external monitors should be getting better with each kernel update (?), and that there were important updates from 6.14>6.16 that explain the improved stability, especially during boot around the time LUKS pops up.

It is possible when Fedora/Ubuntu release with the newer kernels you may not need a separate monitor at first to get through the installation. I also cannot explain why the BIOS was not at least showing up at first either (upon first boot with USB4, prior to HDMI monitor install). Also, this MAY not work with other USB4 (non-Thunderbolt) AMD motherboards. Apparently the way USB4 is activated is through the CPU rather than traditional means in this motherboard/CPU combo. ChatGPT told me I had a higher chance of getting it to work with this combo rather than a motherboard with a native USB4 support (ie, GIGABYTE X870I), why I do not know.