Just to be clear these are on 2 separate pages? You want to have buttons on your home page, that behave like the buttons you created for the tabs. So instead of a 2 step process “click hobbies” → “click tab”. You want it 1 step.
If this is the case the only way I have seen how to save data from transferring from 1 page to another is by using storage
https://www.wix.com/velo/reference/wix-storage
This you could use just session storage and save the name of the tab you want to go to. Then on your hobbies tab you could check to see if there is some data in the session and just move you to that state in the multi-state box much like you are doing now with the button clicks. Except it could store the name of the state directly in the memory so you wouldn’t need conditions.
session . setItem ( “hobbyName” , $w ( “#someButton” ).label)
conditions something like this would set the session variable.