0xChain thank you for taking the time to report this bug!
I have reviewed recent builds as well as the most recent build from the App Store. When switching tab groups (whether they are Private or not), Orion does not preselect a tab, so this is the expected behaviour.
When it comes to opening the keyboard on a new tab (when touching the + button), this appears to have been fixed recently. Would you be able to confirm this works fine for you?
I'll close this ticket as it appears to me there's no work left for us on it.
Thank you for your help in making Orion a better browser!