Unfortunately, there is no official data you may use to analyze this information.
First of all, you can check this information only for your own application in the Google Play developer console, so when you enter the application and go to conversion analysis, you can actually check for which keywords your application gets the highest number of downloads in the particular country. So this can actually help you, for example, in keyword promotion. If you see that the application is getting high volumes for a particular keyword and you understand that the position for this keyword is not top one but top 10, for example, you can use these keywords in keyword promotion campaigns to boost the ranks to top positions, and in such a way the amount of organic search traffic may even increase and become higher due to the fact that the application is occupying top one for now.
But when we are talking about the App Store, there is no way to check for which keywords your application is getting traffic, even in App Store Connect for your own application. First of all, you need to conduct competitor research. Let’s imagine that you have drifting application, so you just put the main keyword like “drifting” and actually analyzes all apps in search. It is needed for you to understand for which keywords each of these applications is in position one, or at least in position three if it is a game. So you can go, for example, to Keyapp, use “Smart campaign,” and check all the apps for the indexed keywords. In such a way, you will know which keywords occupy the top ranks. So probably the applications are getting the search traffic exactly for these requests.
One more method is to analyze the text, such as to see which keywords are added to the title and short description, as these two fields are the most important and most probably the most trafficked keywords will be added there for some competitor apps. And you can use different app store optimization services that actually do the same thing but just show you the analyzed data. Pay attention to the fact that all this data is just assumptions because official information from both stores is unfortunately not possible to get.