[8.x] Improve SearchApplication definition (and related) (#3040)

[pquentin]

Backport

This will backport the following commits from main to 8.x:

• Improve `SearchApplication` definition (and related) (#3040)

Questions ?

Please refer to the Backport tool documentation

[github-actions]

Following you can find the validation results for the APIs you have changed.

API	Status	Request	Response
search_application.delete_behavioral_analytics	🟢	3/3	3/3
search_application.delete	🟢	7/7	7/7
search_application.get_behavioral_analytics	🔴	2/5	5/5
search_application.get	🔴	10/10	6/10
search_application.list	🔴	7/7	2/7
search_application.post_behavioral_analytics_event	🟠	Missing type	Missing type
search_application.put_behavioral_analytics	🟢	3/3	3/3
search_application.put	🔴	3/10	10/10
search_application.render_query	🟠	Missing type	Missing type
search_application.search	🟢	16/16	16/16

You can validate these APIs yourself by using the make validate target.