No the CAC-1587 will not work, it is USB-C -> HDMI. Xbox series X only has HDMI as out put.
You will need the CAC-1334 that is HDMI -> USB-C it supports up to 4K60Hz.
https://www.club-3d.com/en/detail/2572/hdmi_to_usb_type_c_4k60hz_active_cable_m-m_1.8m-6_ft/
I would try the CAC-1336. It might support 4K. It might even support 5K or 6K or 8K30 depending on the GPU and drivers (maybe from a PC but probably not Xbox). I don't think 5K and 6K have been tested by anyone yet. None of the earlier HDMI to DisplayPort adapters support width > 4096. The CAC-1336 might allow USB data which would enable the USB functions of the display but I don't think this has been tested (The CAC-1332 had that function even though the product description doesn't mention it). The CAC-1336 I received produces no signal - I probably need a replacement - so I was not able to test any resolutions, 4K or otherwise, and I saw no indication of USB functionality (no power from the USB-C port and no USB device connection in the OS).