There has been a lot of research done into whether eye strain from up-close work and in particular whether working with screens causes myopia.
In terms of the latter, Scishow did a video in 2018 about whether screens can damage your eyes which addresses digital eye strain with the conclusion being that they do not.
Since then there have been more recent and comprehensive study reviews (2020 and 2021), explaining how scientific trials have found a lot of correlation but have been unable to prove causation:
https://www.reviewofoptometry.com/article/myopia-screen-time-not-linked in (Published feb 2020)
https://reviewofmm.com/what-does-science-say-about-screen-time-and-childhood-myopia/ (published 2021)
A paper systematically reviewing 15 studies: (2020)
The review paper in the last link describes the methodology for their systematic review in this way:
"Data from 15 studies which had explored this association was combined with meta-analysis. The more recent studies agreed on an emerging trend of screen time being associated with myopia. Overall, however, the results of this study were mixed and showed screen time was not linked to prevalent and incident myopia."
In terms of Computer Vision Syndrome, the effects are usually not permanent. The treatments listed of resting and refocusing on a more distant point are thus aimed at relieving or preventing the temporary eye strain and headaches.
Despite the inability to prove causation thus far, there is a high correlation of indoor studies and reading or screen use with myopia in childhood development, which is why many optometrists still caution patients against eye strain through taking breaks.
Reduced Vitamin D from lack of outdoor exposure in youngsters established as a causative link
In further studying this correlation it has been established reduced vitamin D from insufficient time spent outdoors in natural sunlight does have a causative relationship in developing myopia:
Here is some more information on this topic:
Scishow did a useful high-level breakdown on research into the increase in nearsightedness in 2015.
a paper on an experiment done on rhesus monkeys indicating that sunlight helps mitigate the development of myopia.
Interestingly for the earlier topic of eye strain, the SciShow link mentions that computers actually tend to be too far away to fit into the eye strain category, unlike smart phones, tablets and books which are obviously closer - though their video does not seem to factor in other possible factors such as glare and brightness/dimness etc).
Stress-related Myopia as a possible (though rare) candidate
Though the technique of natural vision correction through exercise is debated among eye doctors there still is so far no proof that it works, with the one possible exception being for stress-related myopia,
which the American Optometric Association, although that this is not what is commonly referred to when speaking of myopia.
In that case it seems there are specific eye exercises that would need to be employed, so identifying those from the research would be the key. They describe vision therapy for stress-related myopia in this way:
"Vision therapy is an option for people whose blurred distance vision is caused by a spasm of the muscles that control eye focusing. Various eye exercises can improve poor eye focusing ability and regain clear distance vision"
Mayoclinic mentions that for this type "natural vision exercises that tackle the cause of the problem "can make you less dependent on glasses ... but it helps only a small number of people".
The eye gym might be suitable for this latter demographic though. And for those whose myopia may be due to vitamin D deficiency the outdoor aspect might still be a strong healing factor for the former group.