I suggest donating to your local wild animal rescue/rehabber. They’re all volunteer based. They receive $0 public money. The public rarely sees the work they do. They’re doing physically and mentally taxing work purely for the love of animals.
They typically all have a donation page, and many have Amazon Wishlists where you can send them cleaning, maintenance, or medical supplies directly if you’re worried about the money going to something you might not intend.
Nothing will go to people. You won’t have to question if you’re really help an animal that may or may not exist in a country you’ll never see. They’re your neighborhood animals.
As the !superbowl@lemmy.world person here, I look specifically for a raptor rehabbers to donate to, and I share links to those rescues worldwide.
I can’t find my link to the world rescue database, but for a US based one, you can look here or just Google up “wild animal rescue near me” and you should get some options.
I am a big fan of most zoos too, so I wouldn’t want anyone to write them off completely. As I’ve gotten to learn more about the animals, when I get time to talk to staff now, I’ve been getting more info on the regulations and licensing they have to navigate, and transitioning from a place helping animals to one that also displays animals is a pretty big leap, and that is going to require much more overhead. While many cases won’t be as extreme as a huge zoo like OP was looking at, that would seem to be what leads to larger and larger zoos starting to look more like a typical corporation on paper like that.