This will vary massively from developer to developer - some are much, much slower than others (Spotify I'm looking at you). Do not expect much Siri integration or ApplePay on the web on Day one of GM or Public release.
Apple's guidelines on this are *usually* that no overt reference to iOS 10 features can be made in update notes prior to public release but I *believe* that features can be added covertly from GM onwards.
Compatibility updates are another issue entirely, developers are always free to update their apps to fix anything that iOS 10 breaks whenever - even during the beta process - I've already started to see this.