Does the modern testing theory help solve the misleading nature of drawing conclusions based on the significance or the non-significance of the P-value?
Article Evidence against vs. in favour of a null hypothesis
Article Bayesian alternatives for common null-hypothesis significanc...
https://www.ncbi.nlm.nih.gov/pmc/articles/pmc7275319/
https://www.intechopen.com/books/bayesian-inference/bayesian-hypothesis-testing-an-alternative-to-null-hypothesis-significance-testing-nhst-in-psycholog
Article A Pragmatic Approach to Statistical Testing and Estimation (PASTE)
Depends what you mean by "modern theory testing" (e.g., reporting BFs, the 5sigma rule, replications, machine learning approaches find "best" predictions, registering studies, more plots, etc.)
About which of these alternatives (some of which are not that modern, like confidence intervals). If on how computer have changed inference, I believe the best book is: https://web.stanford.edu/~hastie/CASI/ , which is freely available at https://web.stanford.edu/~hastie/CASI_files/PDF/casi.pdf . It has several useful plots showing how procedures have developed over time. These are focused on inference (so in the preface they describe how this focus is different from the focus of some in so-called machine learning), but drawing a line between inference and prediction is difficult.
Hypotheses are generally tested through using null hypotheses against p-values. However, very limited evidence is available form modern theory testing approach
I seriously doubt that the most scientific way to do research is through p-values: NHST became the baseline for historical reasons and also because it's easy to compute, but it's 2020 there's definitely more out there, it's not 1920 anymore
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