Finger pain from using the trackpad with Taptic Engine.

... it's like poking a wall, all the force of the press is cushioned by the joints in my finger and as a result there is a nagging pain in my finger after a long day at work.

I think you described the phenomenon quite accurately, and the solution is as you wrote: use tap to click instead.

Since there is no physical pressure ...

You mean motion or displacement or (most accurately) acceleration. In their absence, forces are always met with equal and opposite forces. No need to see a doctor; ask a physicist 😄

There is some movement of the Trackpad surface which tries to imitate the physical movement of the older style trackpads...I think they do a good job in that respect. You can tell there is some movement since pressing the trackpad when it is powered off feels rock solid with no movement at all. So you may want to have Apple or an Apple Authorized Service Provider examine your laptop to see if there is a problem with the Trackpad. They also have a Trackpad Calibration service utility which they can run in case your Trackpad is out of calibration.

Edit: You may also need to take some short breaks...anything repetitious for long periods of time is never good. Also consider getting an external mouse or an external trackpad which may be more comfortable for you.