Just as a final update...
So I purchased a new USB-C to DisplayPort 1.4 cable from Amazon - brand name "uni" and supports 8K@60Hz, 4K@120Hz, 2K@240Hz, 5K@120Hz, HRD, HBR3, HDR10, ARC, 32.4Gbps, FreeSync, G-Sync, MST, DSC. This cable was recommended in a forum as being compatible with the Mac Studio for connecting to a 4K DisplayPort monitor.
After running this setup for 2 weeks now I am pleased to report zero issues with the attached TB drives and the display being connected simultaneously. But initially even the "uni" cable did not work until I plugged-in the USB-C plug reversely, even though this should not matter with USB-C. It seems the Mac Studio has some rather funky UB-C ports - as also some USB-C cable plugs fit only loosely while others again are hard to plug-in. And it's definitively rather selective about which USB-C cables it will agree to work with.
sounds like a USB-C manufacturing spec issue if some fit and others don't.