The with sharing keyword on the class declaration enforces the sharing rules that apply to the current user.
This means that the user can only see and modify the records that they have access to based on the organization-wide defaults, role hierarchy, sharing rules, manual sharing, teams, and territories. The without sharing keyword, on the other hand, ignores the sharing rules and allows the user to access all records, regardless of ownership or sharing settings. This can pose a security risk and should be used with caution.
The schema describe calls and the UserInfo Apex class do not directly affect the sharing rules, but rather provide information about the object and field permissions, and the user's profile and role, respectively. These can be used to check the user's access level, but not to enforce the sharing rules on the custom search tool. References:
* Apex Developer Guide: Using the with sharing, without sharing, and inherited sharing Keywords, pages
13-14
* Trailhead: Platform Developer I Certification Study Guide: Apex Basics and Database, unit 3