Coincidentally someone mentioned this video to me the other day (this clip is eight seconds, but maybe you don't want to watch it):
"Tiger attacks mahout on elephant!"
https://www.youtube.com/watch?v=1n-3cFIuQBc

Long version (about three minutes, with a lot of discussion):
"Tiger Attack: The Full Video & Behind the Attack!"
https://www.youtube.com/watch?v=T0kzdu_wTM0

Spoiler: the mahout is OK although he had to go to the hospital. But what surprises me is that you literally can not see the tiger in a big grassy field until a couple of seconds before it leaps onto the guy on the elephant (although one commenter says he could spot it by the grass waving differently where the tiger is). So if you can actually see the tiger, you may be safer in that sense.

I was also very surprised that a tiger would attack someone on an elephant. I expected to see something more like this with the elephant deterring the tiger -- but that is in a different location without tall grass so the tiger can't get close enough to quickly ambush (given cats are mainly sprinters):
https://www.youtube.com/watch?v=fd-SROLWvAw

Or in the USA (where cougars and bobcats drop out of trees):
"Father fends off mountain lion that attacked his three-year-old son in California"
https://www.reuters.com/article/us-california-cougar-attack-...
"Foy said that mountain lion attacks on humans were “extraordinarily rare,” noting that just 16 cougar attacks on people had been documented in California in the past 100 years."

Also:
"Can you spot these bobcats photographed in Wisconsin forest?"
https://ftw.usatoday.com/2021/12/can-you-spot-both-bobcats-p...

So, that is some proof that your fears of large cats are definitely justified -- at least in certain contexts. It is prudent fears like that which have kept people alive for many thousands of years.

Black bears on the other hand, at least in the lower 48 states of US America, tend to be fairly shy and will almost always run away from you -- unless you are between them and a door to escape or between a mother and her cubs. This is because the black bears that did not were all killed long ago and probably eaten by humans. That is not so true up in Canada though, where bears -- especially grizzlies -- have not had that same level of selective pressure recently. Those you should be (prudently) scared of too.

Related:
https://bear.org/why-are-black-bears-so-timid/
"For hundreds of thousands of years—until about 10,000 years ago—North America was home to saber-toothed cats, American lions, dire wolves, and giant short-faced bears. Black bears didn’t stand a chance against any of these predators in a fight, but the black bear was the only one of them able to climb trees. Black bears stayed near trees and lived by the rule “Run first, ask questions later.” They develop a mind more like that of a prey animal than a predator. Today, the black bear’s timid attitude aids survival in the face of grizzly bears, timber wolves, and people."

Coyotes can be scary too:
https://en.wikipedia.org/wiki/Coyote_attack
"Coyote attacks on humans are uncommon and rarely cause serious injuries, but have been increasing in frequency, especially in the state of California. In the 30 years leading up to March 2006, at least 160 attacks occurred in the United States, mostly in the Los Angeles County area. Data from the USDA's Wildlife Services, the California Department of Fish and Wildlife, and other sources show that while 41 attacks occurred during the period of 1988–1997, 48 attacks were verified from 1998 through 2003. The majority of these incidents occurred in Southern California near the suburban-wildland interface."

Anyway, this is all is not completely idle curiosity for me as I live in a nature park with bears and bobcats and coyotes and such -- and was concerned especially about bobcats and coyotes when my kid was young.

Realistically though, dog attacks in the USA are way more common these days:
https://en.wikipedia.org/wiki/List_of_fatal_dog_attacks_in_t...
"Fatal dog attacks in the United States cause the deaths of about 30 to 50 people in the US each year, and the number of deaths from dog attacks appears to be increasing. Around 4.5 million Americans are bitten by dogs every year, resulting in the hospitalization of 6,000 to 13,000 people each year in the United States (2005)."

If you ever have been attacked by something, one possible way to deal afterwards with the trauma -- not involving psychedelics -- is Se-REM, an audio version of EMDR:
"A Self-Help Version of EMDR Could Make Healing from Trauma Easier"
https://www.madinamerica.com/2021/07/self-help-emdr/
https://se-rem.com/