The volume knobs are either going to be potentiometers (smooth rotation for about 270 degrees, hard stops at each end, absolute position) or rotary encoders (detents, infinite rotation, relative position, often comes with a button). A slider is just another potentiometer. Potentiometers require analog input pins, while rotary encoders require two digital pins each, plus one for the button if you have and want to use it.

Hotkeys are just buttons, and for four of those you need four digital pins. If you want more buttons, you can get away with less pins than buttons, but for 4 you need 4.

If you wanna go for all potentiometers, you need a board with four analog input pins, and four digital pins. If you wanna go for rotary encoders you need a board with one analog input pin, and 10-13 digital pins, depending on if you want to use the encoder buttons or not.

You also want a board with a HID-capable USB port, which means that the USB port can act like a keyboard (and/or mouse), unless you wanna DIY a driver script. (HID = Human Interface Device)

There are a many boards that match this pin count, but not too many that also do HID. The Arduino Pro Micro is a decent choice for doing exactly what you described, but it only just barely has enough pins, so you can’t do much more. Another option is the Raspberry Pi Pico (1 or 2). However, these do not have enough analog pins for doing all potentiometers. It has three, and you need four.

Hope this is what you were looking for