At my workplace, back in the day, workers exposed to hydroquinone would undergo occupational health checks to monitor adverse effects. As far as I can work out, this involved a nurse checking skin and eyes for any visible signs of discolouration.

Does anyone still do this? Is it required, given WEL and PPE requirements are adhered to?

Well, this is just COSHH: if you are going to use this substance ideally you prevent exposure to it using stronger controls than PPE. If you have any reason to believe that  people are being exposed to it, you should monitor this exposure through a system of health surveillance.( COSHH Regulation 11- Health Surveillance). The WEL is not that relevant here; you really need to limit the exposure to  Hydroquinone to as low as reasonably practicable.