The DS4 is simply a DirectInput controller recognized by the OS as a HID when connected to a PC. This makes it compatible with a wide range of Windows versions, including 98, and most of the time it works well enough with it. The issue is how Sony programmed the controller under DirectInput.
It's recognized as a gamepad, not joystick, thus making the analog sticks digital in games like Le Mans 24 Hours (Eutechnyx, 2000). The original NFS and Sports Car GT on the other hand have issues with the accelerator, as the Z axis is mapped to the left and right movements on the right stick. On top of that, the triggers are mapped as sliders which are always pressed, meaning you would have to press them in case you wanted to stop accelarating or braking, if mapped to do so on NFS Porsche Unleashed.
The solution would to natively map the buttons and axis identically to the ones on the Xbox 360 Controller, which despite the criticism towards the mapping, has the ideal setup for old games with buttons 1 and 2 mapped to A and B (also making menu navigation with a controller in line with what's used today for games that support it) and the triggers as different polarities of the Z axis.
But how could that be done? Older OSes do not support reWASD and the like, so is the solution somehow rearanging the settings through the DirectX APIs or desoldering the chip which contains the data in interest here and trying to reprogram it externally?