Is there an equivalent scale in UX as the Cooper-Harper Scale or the Cooper-Harper Ratings are in Handling Qualities Engineering in Aerospace? The Cooper-Harper scale associates a quantitative value to the ability and ease of completing a task in prefer and acceptable ranges such as time to complete task or the precision of the task as well as how easy was it to meet or exceed those criteria?
Yes, there are modified Cooper-Harper Scales that measure operator workload. It involves some basic tweaking from "pilot" to "operator".
Here is one such representation of the Modified Cooper-Harper Subjective scale:
I used these modified scales many times to measure acceptable operator workload for multiple defense department and aerospace programs, which didn't target a pilot.
One of the advantages to this simple modification is that many are already familiar with the source material. Especially if you are dealing with aerospace or defense department programs. The ability to demonstrate workload on a scale that is already familiar makes telling your story easier.
If you want to measure the cognitive workload the most famous scale is NASA-TLX scale. SWAT is other one which is widely used. However they are multidimensional which means mental workload is calculated based on more than one scale, unlike Cooper-Harper.
If you want to measure the usability you can use SUS scale, which is the widely approved and used for usability evaluation.