wuzak
Captain
They reduced manifold pressure to shift because the gears had to mesh and its both easier and less stressful to mesh gears at lower speeds than it is at higher speeds. Anyone who has ever shifted a manual gearcase will recall that. It's in all the two-stage pilot's manuals to reduce power to shift supercharger gears, and turbocharger gears operate the same way. It would be different, of course, if the coupling were hydraulic.
Like regular gearboxes, the gears are always in mesh. The clutches are used to engage or disengage the gears. In regular car manual gearboxes this role is done by the syncromesh.
Still, even when shifting something like a Formula 1 transmission, they momentarily remove power from the geartrain by interrupting the ignition to ease the gear engagement. Every single button-operated motorcycle gear changer I have used (several) has had ignition interruption, too.
Current F1 transmissions have zero power interruption.
Sequential gear systems used on racing touring cars, for example, do have ignition cut for upshifts, and can be operated without using the clutch. Some Supercars drivers only use the clutch pedal for the start of the race and in the pits.
These transmissions tend to not have synchromesh, but rather have dog rings for engaging gears.