I was able to find the commit that introduced this change and it contains the following text:

Some Compose platforms (web) don't have blocking API for Clipboard access. Therefore we introduce a new interface to use the Clipboard features.

The web clipboard access is asynchronous, because it can be allowed/denied by the user:

All of the Clipboard API methods operate asynchronously; they return a Promise which is resolved once the clipboard access has been completed. The promise is rejected if clipboard access is denied.