I can confirm that the USB hub built into Dell U3821DW doesn't work with Mac Mini M2 Pro (Ventura 13.2.1) irrespective of how the monitor is connected. None of the USB peripherals are recognized or available to the Mini. This situation doesn't change whether the monitor is connected via the Apple Thunderbolt 4 Pro cable or if extra USB 3.2 (Gen1) cable is connected from the monitor upstream port to the Mini. For example, my Blue Yeti X microphone and Logitech C920 webcam plugged into the monitor USB hub aren't available to the Mini.
In contrast, all USB ports built into the monitor hub work flawlessly when the monitor is connected via the same Apple Thunderbolt 4 Pro cable to a 16-in 2019 Intel MacBook Pro (Monterey 12.6.3). The built-in USB hub also worked correctly when the MacBook Pro was previously connected via a USB-C to DisplayPort cable plus the upstream USB cable to carry data.
Besides the fact that monitor settings remained the same between the two hook-up, no amount of fiddling with monitor menu settings could change the outcome. I'm left to conclude that Dell U3821DW monitor built-in USB hub isn't available to Mac Mini M2 Pro users running Ventura 13.2.1.