As I said, the users.php screen is not capable of displaying post search results. Even if it did, you’d lose the users while posts are being displayed, so you’d be changing the page anyway.
It is possible to add view links which are used to display users in certain roles on users.php. I don’t think added views have to be links, one could probably add HTML for a custom post search box. It’s not feasible to add another search box in the upper right corner or alter the existing one.
It’s also possible to add HTML content after the “Change role to…” dropdown and button. Where ever you add a custom search box, you could use JavaScript and the API to get search results and display them in a modal or pop-up box. It’s the only way I can see doing a post search without leaving users.php.
I’ve no doubt such a feature would save you time, however, developing such a solution would take much time and effort. What I would do in your place is simply keep two browser tabs open. One for users and one for posts. If I’m on the users.php and need to search for a post, I’d just jump to the other tab and do the search there, then switch back afterwards. If the post search box is currently active, the two tab approach doesn’t involve any more clicks than a custom search box with modal would take. It does initially take a couple extra clicks to set up the two tabs when you begin working, but after that there’s no extra effort involved and a lot less development effort.