When it comes to utility-scale grid storage, Tesla definitely gets the most press, but I would agree that there are serious competitors like AES and Vestra. I would be interested to hear some names from your endlessly long list, because I can't come up with many of them. For the home battery market, Tesla is definitely one of the leaders.
I think the primary reason Tesla has not shipped more batteries that are permanently attached to the grid, either in from or behind the meter, is that selling a car is a far higher margin destination for their batteries. So as long as Tesla car sales can suck up batteries, the battery factories are probably going to be using most of their time making batteries for cars.