Something that Firefox and Chrome have in common is the ability to limit which extensions run in Private Browsing mode. The default is to not permit an extension in Private Browsing mode, unless manually and expressly permitted to run in private browsing.
This doesn't seem to be the "done" thing in Safari though, but there may be a case to be made for considering it.
If people use Orion for its plethora of extensions via Chrome and Firefox stores, they will no doubt at some point start adding untrustworthy ones that collect data. While those stores might try to stop this, if someone is in private browsing, they likely are trying to signal they'd like to try limit what is being exposed. Limiting which extensions run in this context perhaps makes sense? On the other hand, maybe it will confuse them if extensions aren't available in private browsing mode until they enable them?