Why isn't USB redirection working for my Pi-connected peripheral?

There could be application/mode-specific reasons for this - you may wish to check other Knowledgebase articles specific to RDP mode and Horizon mode first.  However, there is another reason why you might be having trouble, namely that your USB peripheral isn't receiving enough power:

The Raspberry Pi is a very low power device that is incapable of drawing more than 2.5 amps at 5 volts (if using a micro-USB connector at any point in the power delivery chain) or 3.0 amps at 5 volts (if using only Type-C connector(s)).  This is a limitation of the physical interface.  If you connect a Pi to an unpowered USB hub, this amount of power - minus what the Pi itself needs - is almost certainly not sufficient to guarantee the required amperage (500mA for a USB2 port, 900mA for a USB3 port) on every port of the USB hub.

What that means is that your Pi may not be able to adequately power an unpowered hub, especially if it's a USB3 hub, or if you have USB devices connected to the hub that have a high power draw, e.g. storage devices or WiFi dongles.

If you are connecting USB devices that are built in to your monitor, you might not even be aware that you are using an unpowered hub, but you almost certainly are (rule of thumb: if the other end of the USB cable connected to your Pi is any type of USB-B connector (whether full size or micro), then you are connecting to a hub).  Despite the fact that monitors are connected to A/C power, in order to save a few cents monitor manufacturers never power their internal USB hubs (which personally I find pretty despicable, but I suppose there is a lot of competition and their profit margins are really, really tight).

Wherever possible, you should try to connect peripherals directly to the Pi rather than via a USB hub.  If that's not possible (e.g. peripherals built in to a monitor) or if the peripheral is very power-hungry (e.g. spinning hard disk), you need to connect via an independently-powered USB hub.  Unfortuately that might mean that you need to connect an unpowered USB hub in your monitor to a powered USB hub, and connect that to the Pi.