For real-world applications outside engineering and academia, I would rely heavily on confidence intervals and/or confidence bands. For example, the packages from easystats [1] in R have quite a few very useful visualization functions, which make it very easy to interpret results of statistical tests. You can even get a textual precise description, but then again, that's intended for papers and not a wider audience.
Apart from that, I would mainly echo recommendations from people like Andrew Gelman, John Tukey, Edward Tufte etc.: Visuals are extremely useful and contain a lot of data. Use e.g. scatterplots with jittered points to show raw data and the goodness of fit. People will intuitively make more of it than of a single p-value.
Would the policy be "look at our confidence intervals later and then decide what to do"? One remaining issue is how to have consistent decision criteria, and to convey it ahead of time. Imagine a context with 10-50 teams at a company that run experiments, where the teams are implicitly incentivized to find ways to report their experiments as successful. Quantified criteria can be helpful in minimizing that bad incentive.
About the stupid or harmful nature of null hypothesis testing in general, what do you recommend instead for decision making and for summarization of uncertainty? In the scenario of large (yet fast moving) organizations where most people will have little stats background.