TL;DR It depends on what you consider sensitive data. To be safe, get the URL using your browser in private navigation / incognito mode with all the extensions disabled.
Besides the query in the search box, the URL might contain parameters with data about the search results you clicked, filters, topics, display language, stuff added by extensions and other software under certain circumstances. Some tracking parameters, rather than tracking you specifically, are tracking how users land on specific pages based on timestamps or algorithms that differentiate users from others but do not identify them as specific persons. These IDs count unique views, aggregate log errors and bug reports.
As of October 2023, many applications include a Share button; it's worth noticing that Chrome shows a Share button in the address bar for many pages but not for Google Search results. Also, it's worth noticing that the Google Search results page on the desktop doesn't include a Share button to share the page but includes share buttons on several of its elements. Below are a couple of examples:
If you are unsure about the meaning of the URL parameters, repeat your search in private / incognito mode or use the Google mobile app and the Share button instead of copying the URL.
Besides privacy and security concerns, consider that some parameters might not work as they do in your device on your acquaintance's device.
URLs might generally include parameters from other sources besides the web application and the "plugins" it might be using, like Google Ads, Google Analytics, Facebook, etc. Extensions and other local stuff might modify the URL, several handled through the built-in web developers' tools.
Google allows users to sign in using multiple accounts simultaneously. When using this feature, Google will use a URL variant (adding /0/, /1/, etc. to the URL used by users signed in using only one account) to handle which account is the active account based on the order in which the accounts were signed. This works together with cookies.
Suppose your acquaintance is also using a sign-in account feature, and the URL being shared points to a resource that is not shared with anyone, and the account that matches the index included in the URL hasn't been accessed. In that case, it will tell that they should request access in some cases, but in others, it will throw an error that might tell the user that the file doesn't exist when it does.