In a time trial this wouldn't be particularly valuable information since each cyclist starts at a different time. If you are able to catch the racer in front of you, they are probably not your primary competition. I couldn't speak to triathlons.
In a road race, the information could be useful when bridging to a breakaway. In that case, the information should be displayed on a bike computer, or for a pro that is already wearing an earpiece I guess audio would work (glasses display would be too distracting). I'd want it to tell me given the pace of the break and my current pace how long would it take me to catch the break. Then I could gauge if I could hold the effort long enough to bridge successfully.
Are you going to make a prototype for your project? If so what tech are you using (lidar, just cameras, radar, mm wave)? Have fun with this.