As suggested in https://wiki.openstreetmap.org/wiki/Key:toll, I added a "toll" tag to the HOV lane. I chose against marking the HOV lane as a toll lane, since the lane is mapped as a separate way (see earlier comment for a potential explanation why this lane was mapped as a separate way). I will take a look around to see if the exit junction can be moved or modified so navigation apps such as OsmAnd stop telling drivers to "take a right onto Exit 12A" even when drivers want to stick with I-880 north, because that is just confusing.