Is it obligatory to search for a paper with a Quranic verse that was buried and has not yet been found, and does a person become an infidel if they do not search for it?

If the paper was buried in a clean place, away from people's path, then you have fulfilled your duty. If you did not do so, it appears that you acted with good intentions, without intending desecration. Therefore, do not burden yourself beyond your capacity, and do not disbelieve in what was mentioned. We advise you to disregard these whispers (waswas) and to dispose of such papers through legitimate means.