I assume every time you open a post page from a search result page, there is a search query run simultaneously as or before the post page is loaded, judging from the "q" parameter in the query string of the resulting post link URL. (Example: Opening post #4257394 from touhou results in the URL https://danbooru.donmai.us/posts/4257394?q=touhou).
Again, I assume this is to facilitate the post navigation functionality on individual post pages.
When "Enable post navigation" is disabled in a user's settings, does the query parameter actually provide any additional functionality to the user?
If not, I would suggest disabling running the previously assumed search query when the setting set to 'disabled', as well, in order to cut down on unnecessary search queries being run.