I know I've heard of this but I have never seen a turbo setup on a stern drive motor.

mercruiser does

if you look up Thailand long boat racing you will find a ton of them!

Mercruiser does as noted, some people have attempted some shade-tree mechanic versions, but from what I have seen the exhaust manifolds required are just pretty complex, and dealing with the heat, and other issues has kept most people going with superchargers as far easier.

I've seen several turbo big blocks running thru transmissions into TRS drives back in early 80's
A friend had a Gale Banks kit on 454's on a Scarab. And I knew a few other guys with em. Heat was an issue, and we added a lot of extra vents and louvers on the Scarab.

In recent times, turbos aren't nearly as popular compared to superchargers because it's about impossible to "Coast Guard Certify" a turbo kit fir an enclosed engine compartment. PLUS Bravo drives aren't happy campers with more than 500 ft lbs of torque.

A supercharger is easy to "certify" for marine use. A supercharger kit that gives you 550 to 600 ft lbs of torque is much cheaper than an Engineered turbo system because no exhaust modifications are "required" on a supercharged motor. By the time you justify the added costs of a turbo setup you're making 700 ft lbs of torque and you won't have a reliable boat until you add $25k worth of upgraded outdrives behind each motor.

My friend build 502mag mpi, twin turbo, charge cooler engine to 27 VIP Vindicator. It’s bravo boat, clever throttle use it keep one piece last summer, no problems. Heat remove of every exhaust part is complicated but works well after all parts are water cooled.

I think Mercury sold a couple of their turbo motors, couple two tree. Overall they were a huge flop. Everyone is on to miniature nuclear reactor propulsion now.

Mini Nuke reactors are so 2000 and late. Zero Point Modules or bust.