Rice – How to do if I have added extra water in rice for braising and you can see the rice is turning into sticky rice

There shouldn't need to be any variation in the water at all, since the things that you are adding are already hydrated and are not taking in any water. Indeed, it would be possible that some vegetables might even give off water.

I would be more inclined to look to whether you are measuring accurately every time you use the rice cooker (just asking) and then, if so, whether your rice cooker is consistent. I had an inexpensive rice cooker that I liked for the convenience, but it was inconsistent on turning off, so the results were a little too varied, OK for me, but not when I was serving other people.

The only other thing to consider is that many rice cookers work on a temperature principle...when the temperature starts to rise (meaning the water has been absorbed) the cooker shuts off. If the ingredients you are adding are raising the temperature of boiling (as in a lot of salt, say) then it is possible that you cooker is shutting off before the rice is cooked, and then the water is absorbed or evaporates, but the rice cooks no further.

I would pay very close attention to your measuring (rice and water) for the next couple of batches and see if that fixes the problem.

Based on your edit, my best guess is that this particular rice has a really high amount of surface starch, which gelatinized when you first tried to cook it (liquid from the mushrooms might have been enough to get this result). That would have created a moisture-resistant layer around the grains that inhibited moisture from soaking in further. Your soak would have washed that away and allowed the rice to properly absorb the broth.

That's definitely weird - probably a byproduct of how this particular brand gets processed. A further experiment worth trying would be to briefly rinse off the grains in a colander for your next batch. That would also get rid of surface starch without quite the same effect as a soak. If they work after even a brief rinse, I'd consider that pretty good evidence for this theory.

Another thing you could try might be sauteeing the rice in a completely separate pan from the mushrooms, so that they're exposed only to oil and the surface starch gets toasted instead of gelatinized. Maybe not quite as desirable from a flavor perspective, and of course you'd have to clean another pan, but it's worth testing if you really want to figure out the root of the problem.