How would we find out if this passageway is open?
As Christine said, that nifty shortcut is for going directly from Sistine into St. Peter's, not to the Sistine from elsewhere in the museums. it's only accessible for tours, and only those which specify its use in their tour descriptions. The Vatican Museums don't offer a combo museums + basilica tour themselves so booking through one of the better independent companies is necessary for this benefit. Here are a couple of for-examples:
https://theromanguy.com/tours/italy/vatican/sistine-chapel-vatican-tour?
https://www.througheternity.com/vatican/private-sistine-chapel-tour?_gl=1*yoqgp5*_up*MQ..*_gs*MQ..&gclid=EAIaIQobChMIlY3g5-GNkwMVezUIBR1cXgSAEAAYAiAAEgLum_D_BwE&gbraid=0AAAAADRUUBTbb_dCrA-LYcjfKzBssU2Ax
https://www.walksofitaly.com/vatican-tours/complete-vatican-tour/
Note that all 3 have disclaimers in the event of special religious services that may affect the ability to use the shortcut: stuff happens. This example from Walks of Italy:
"Please Note: The special access passage between the Sistine Chapel and St. Peter's Basilica is not available on morning tours at 8:45am, 9:45am, & 10:15am on Wednesdays and Saturdays. It is subject to other unexpected closures during special celebrations/festivities, including the Easter ceremonies. On such days we will instead explore more of the Vatican Museums' galleries."
The Wed. morning closure of the passage is standard for all tours which would otherwise use it.
The tours sampled above don't include the gardens.
Expect both museums and basilica to be very crowded.