While you won't find a standard download link on the Microsoft Store or Google's website, you can create a dedicated desktop experience using these methods:
Windows 10 includes built-in tools that can perform similar functions without needing a Google-specific download: How do I use Voice Search on PC? - Google Help
Ensure the toggle for "Sites can ask to use your microphone" is turned on.
Visit google.com and click the Microphone icon on the right side of the search bar. System-Level Alternatives on Windows 10
If you just want to use your voice to search on Google Search, follow these steps to enable the microphone:
If you specifically need the Google Voice calling service, navigate to voice.google.com. An install prompt will appear in the address bar, allowing you to pin the app to your Windows 10 taskbar.
Searching for "Google Voice Search download Windows 10" can be confusing because there is called "Google Voice Search" for PC. Instead, you can access this functionality through browser settings, Progressive Web Apps (PWAs), or system-level speech recognition. How to "Install" Google Voice Search on Windows 10