> It's not clear if the API will be public for other browsers or applications to use.

Apple has already confirmed that other app traffic will go through iCloud Private Relay “no matter what networking API you're using”, with some exemptions:

> Not all networking done by your app occurs over the public internet, so there are several categories of traffic that are not affected by Private Relay.

> Any connections your app makes over the local network or to private domain names will be unaffected.

> Similarly, if your app provides a network extension to add VPN or app-proxying capabilities, your extension won't use Private Relay and neither will app traffic that uses your extension.

> Traffic that uses a proxy is also exempt.

From https://developer.apple.com/videos/play/wwdc2021/10096/.