Malinois are very high energy. That's what my dog is. Gotten as a pup in ignorance of the breed (like so many pet owners). We trained each other. Backyard time was laughable. He needed, demonstrated more. .He walked over 100# of me. How? By getting a sexagenerian (60+) to train for half marathons! We went through puppy school for 6 months before he was successful. Then another 2 months of advanced training. That pup got loose in Petsmart. It took a long time to catch him. Run, stop, slide, pivot, repeat. I discourage people out of getting a Malinois. But all they see is sweet, intelligent well trained pooch. Not the months of constant training and commitment. Just like they see a fairly well mannered, sweet, talkative CAG. They don't see the work, and commitment there either! Coexistence can be done. Not easily and definitely in need of constant, daily even by the minute reinforcement! But it can be done. The cats were easier. They required a squirt bottles and water guns strategically placed for quick use.
I knew what I was getting into with mals, because I was already going to a bitesport club with my working line GSD. But yeah, I really wish they weren't available for the average pet owner. They really aren't pets. They can be pets TOO, but they need a job FIRST. And not just months of training, YEARS (forever, really). My youngest is 3, and she still has puppy brain, and the same energy. You can train them, but they will always be malinois. I have three (technically two, and one Dutchie, but in all reality, Dutchies are just brindle malinois). Anytime someone tells me they want one, I've offered to let them watch my youngest one for one day. And although she is far and away the craziest, she's also the easiest of the two registered mals, because she isn't as sharp as my oldest one (one thing I mean about always being mals). My dogs are specifically bred for mid-high level sport though, so they are on another level from even some other mals, either show line, or "pet" line.
And, while I am very much not a cat person, I do agree that they are easier to train around prey animals than malinois. And once you have one trained, they mostly just teach each other, I very rarely have to step in these days. One thing that helps is that my house is actually very quiet and calm, 99% of the time, except when I instigate (which does happen, lol). So all the animals (including the birds!) learn that is how we act in my house, because it's what they see. And it mostly just happens. The dogs are the only ones that need that specifically taught to them.
The big thing, as I was explaining to someone on Reddit, with predators and prey animals, is that they shouldn't ever even get to the point of full on hunting a bird. There's hundreds of steps before that, where they are starting to pay attention, and then focus, and then starting to think about stalking, etc., where the behavior SHOULD be stopped. If you can catch it then, while it's just the beginning of a thought, that's how you can teach them to consider each other furniture. So, one mistake doesn't lead to a dog hunting a bird, it leads to, say, maybe a fleeting glance while the bird is in its cage. It takes hundreds of stacked mistakes to lead to a loose dog hunting a loose bird. But, it's important to know how to read dogs. I've been training competitively since I was a kid in 4-H, and also worked with dogs professionally for almost 15 years. But anyone CAN learn it.