Applications can be opened by mimi type or URL Scheme. Except for PDF files the search results only contain materials resisted with IANA to be used by the browser. Google does not list links to custom URL schemas.
Content is King over bounce
If the visitor to your site hits the back button in (normally) a short amount of time and goes to the next site or searches for the same material ... your URL was not the answer that the visitor needed.
If the user spent time on your content and when returning to Google looked for something else your content satisfied the user.
A bounce is an unsatisfied user. If the user is happy with your content, Google is happy and if the content fills it goal with you ... that is a three way win.
Web applications or WPAs
Web applications remain in the browser thus are cross platform browser applications (although you can register file types to WPAs), and you can setup Analytics within the application.
Details of using analytics from applications are available from Google analytics support pages ... https://support.google.com/analytics/answer/9304153?hl=en
Should you use analytics within a application is another question. Many people, organizations, and countries are looking hard at user privacy in user applications. Google has come under heavy criticism within the EU - even to the point of dynamic linking of web-fonts.
Reference: How can I use Google web fonts statically instead of dynamically?
To be listed in Google's Play Store you must honor user privacy:
And Apple Store's App Privacy requirements:
I personally am not comfortable in today's climate with tracking users usage of applications. But the technology exists to do it. WPA and native applications have access to the internet and can be interfaced to analytics.
Open local files by file type with WPAs
Reference Google's Web.dev for WPAs to open files by extension types, (note WPA are a working draft and the standard requires other browsers to support what Google puts forward) ... https://web.dev/file-handling/
To open an native application with URL Schema
To open an application from a web link the URL scheme needs to be changed. For example mailto:[email-address], ftp:[url], [phone-number].
An official guide for these URI Schemes exists here: https://www.iana.org/assignments/uri-schemes/uri-schemes.xhtml
The application of course must be build for each operating system; but for an idea ... The details for doing so may be best asked at Stack.overflow.com IE https://stackoverflow.com/questions/3057576/how-to-launch-an-application-from-a-browser but for reference but a list of steps is listed here (for Apple IOS native application): https://coderwall.com/p/mtjaeq/ios-custom-url-scheme
Step 1 Go into your app's info.plst file.
Step 2 Add a Row to this and call it "URL types"
Step 3 Expand the first item in "URL types" and add a row called "URL
identifier", the value of this string should be the reverse domain for
your app e.g. "com.yourcompany.myapp".
Step 4 Again, add a row into the first item in "URL types" and call it
Step 5 Inside "URL Schemes" you can use each item as a different url
you wish to use, so if you wanted to use "myapp://" you would create
an item called "myapp".
Google is not going to index URL scheme in search just because it finds them so these will not be indexed by Google.
To Open an application based on Mimi types
Again IANA lists the official assignments and browser has some documentation https://developer.mozilla.org/en-US/docs/Web/HTTP/Basics_of_HTTP/MIME_types
Again the application needs to be installed on the OS ... here is a how to question from unix.stackexchange.com https://unix.stackexchange.com/questions/565353/how-to-associate-a-new-custom-mime-type-with-files-based-on-file-extension
But Google is not going to be providing any custom mimi types to open an application in their SERP and taking over a assigned mimi would resolute in angry people. You would need to provide the mimi type from your own server.