I bought the
CalDigit TS4 Thunderbolt 4 Dock - 18 Ports, 98W Charging, 3x Thunderbolt 4 40Gb/s, 5 x USB-A, 3 x USB-C (10Gb/s), 2.5GbE, Single 8K or Dual 6K 60Hz Displays, Mac, PC, Chrome Compatible with 0.8m Cable
If you don’t mind me asking, what do you mean by the “did not pipe a second display port”
The laptop has a Thunderbolt controller that connects to the Thunderbolt port. The Thunderbolt controller sends signals to the Thunderbolt port. The signals can be USB, DisplayPort or Thunderbolt depending on what is connected to the Thunderbolt port. A Thunderbolt signal can include tunnelled PCIe and tunnelled DisplayPort. To transmit a DisplayPort signal or tunnel a DisplayPort connection, a DisplayPort output from the GPU must be connected to a DisplayPort input of the Thunderbolt controller. To tunnel two DisplayPort connections (for two displays), a second DisplayPort output from the GPU must be connected to a second DisplayPort input of the Thunderbolt controller. PC laptop manufacturers often cheap out on this point. You need to find a laptop that specifies two displays from a Thunderbolt port, or that specifies Thunderbolt 4 which is guaranteed to allow two displays from a Thunderbolt port.
Your laptop has 3 display outputs: the internal display, the Thunderbolt port, and the HDMI port. The GPU only supports 3 display outputs so the only way it could connect two outputs to the Thunderbolt port is if it added a switch between the HDMI port and the Thunderbolt controller. A switch adds cost and takes space on the motherboard.
Can you verify that the TS4 Thunderbolt 4 Dock is connected properly as Thunderbolt? You should be able to see the 2.5 GbE controller in the Device Manager (view by connection) as a PCI device under a Thunderbolt PCI bridge.
One way to connect two displays to a single DisplayPort connection is to use an MST hub, but this will halve the output for each display from 4K60 (or 5K47) to 4K30 (or 5K23). I don't know what the lowest refresh rate the Apple Studio Display can support. Someone will have to test with some custom timings. I think you might prefer trying to get a USB-C signal from the HDMI port using a CAC-1336.
Another way is to not use DisplayPort. Instead, use USB. A DisplayLink adapter is a USB adapter that can output a DisplayPort signal. It uses compression to transmit video from the CPU to the display. 4K60 (12 Gbps) is compressed to ≈ 1 Gbps. It's not great for gaming or video.