They do have...if you do a google search it will come up or stop by a Yamaha dealer. Lower Unit ยป Yamaha Maintenance Matters
With that said any lower unit lube with the same spec will work. You definitely have water intrusion if it's milky. Could be one of the service screws did not seal right? But it usually is the shaft seal. I would pull the prop and make sure there is not fishing line wrapped up around the shaft,refill the unit,make sure the back of the screws and the surface they seal on are smooth and the gasket or washer they use is intact. Take it out for a few hours and test the oil again after words. If if the oil looks good then I would just keep using it and checking periodically. If after a few trips it all looks good....I would run with it but still check it occasionally.
There may be some other recurrent problem a Yamaha mechanic or someone with specific experience may know about
If you still get water going to have to have a new seal and the shaft will need checked to make sure it did not get bent on a prop strike. New seal won't last if shaft is bent.