The vast majority is plant matter. It wastes a lot of energy to chase prey. Plants don't move much. Last I read it was on the order of 80% plants, with a lot of insects being most of the meat.
You may be right that the majority is plant matter, but in salmon season bears gather at salmon runs and waste little energy in snatching fish as they leap up the cascades. See [1]. (Although individual bears do compete for the best fishing spots, they are in a "fish in a barrel" situation when they get one. They don't have to chase anything, just grab and chew.)
Here's an article [2] from 2018, How many salmon will a bear eat?
Excerpt: Adult male bears on Kodiak ate the most salmon on average, consuming an incredible 6,146 pounds (2,788 kg) per bear per year! Adult females ate 3,007 pounds (1,364 kg). Salmon consumption varied among subadult bears, independent juvenile bears between 2.5 and 5.5 years old. Subadult females ate 1,248 pounds (566 kg) while subadult males ate 1,305 pounds (592 kg) of salmon per bear per year.
costs a lot to feed bears. this years salmon price is estimated at $14-20\lb. if we take the average, a bear eats more then $100k a year worth of salmon.
While that is true for inland brown/grizzly bears, the coastal brown bears under discussion in this article eat huge quantities of spawning salmon during the summer and early fall.
They get much larger and much fatter than the inland bears as a result.
More than 20% for many inland grizzly bears, e.g. Yellowstone:
Approximately 45 ± 22% (equation image ± SD) of the assimilated nitrogen consumed by male grizzly bears, 38 ± 20% by female grizzly bears, and 23 ± 7% by male and female black bears came from animal matter.
