How can I stop my Geberit flushing system from hissing?

The issue is more likely to do with the linkage for the actuator, than the actual flush valve or full valve. Make sure the plastic pins that contact the flush actuator buttons are not too long. They can be “off” or slightly too long by a very small amount, Causing the issue. Also, make sure the actuator is installed so it fits flush to the wall, all the way around. If it won’t sit flush, it could be because the flush linkage is a bit long, causing the issue.
There is also a diaphragm located at the top of the fill valve. It’s an easy and inexpensive replacement part. If you’re already in the carrier, you may as well change it. The flush valves usually aren’t an issue with these.
The top of the fill valves are designed to leak into a small tray to act as a counterweight for the fill valve to stop gradually.

The flapper might move a little to the side when flushing, so you fix it it manually. Have the same thing with my TOTO 1.4 gpf. Changed the flapper several months ago, the hissing stopped for a while, now started again. I washed the flapper with lemon juice and soap to remove any calcium carbonate that might accumulate - it reduced the frequency of the hissing but didn't solve it completely. I guess it is the flapper/flush opening contact that got lousy. Maybe a thin gasket would do the trick. Tell you when I check.

Good luck!