So, Google's "Find My Device" service, including its "ring" feature, is not publicly exposed via an official API. This is embedded natively in the Google ecosystem and is used by an end-user through the web interface or mobile app.
Why Google Keeps This API Under The Hood
Disruption of user privacy and security — Making such APIs public can result in misuse which can breach the privacy and security of the user.
Domain-specific: It is a feature that is only useful for users with Google accounts to control their devices, and exposing it as an API would compromise safety.
There Are Other Workarounds: You can already find your device via the web and with an app for most use cases, so an API is less critical.
Workarounds
Only if you need to programmatically activate the ringing feature (or similar capability) do this,
For example, third-party EMM or MDM solutions (like Microsoft Intune and Google Workspace Admin SDK for enterprise users) come with APIs to control the devices remotely. But they may not have the “ring” feature.
Custom App: If you have access to the devices you want to control, you could write a custom app that has permission to control the device and play a ringing sound via your code.
Conclusion
For personal use, you’ll need to go through Google’s existing “Find My Device” interface. For such organizations, enterprise solutions can probably offer equivalent functionality in their respective realms, stay away from. You may want to look for alternative approaches or consult the Google support if that is critical for your application.